Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\left(x^{2}+1\right)}{\left(x^{4}+1\right)} d x=?$ A. $\frac{1}{2} \tan ^{-1}\left(\frac{\mathrm{x}^{2}+1}{\sqrt{2} \mathrm{x}}\right)+\mathrm{C}$ B. $\frac{1}{2} \tan ^{-1}\left(\frac{x^{2}-1}{\sqrt{2} x}\right)+C$ C. $\frac{1}{\sqrt{2}} \log \left(\frac{x^{2}+1}{x^{2}-1}\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin x}{\sin 3 x} d x=?$ A. $\frac{1}{2 \sqrt{3}} \log \left|\frac{\sqrt{3}+\sin x}{\sqrt{3}-\sin x}\right|+C$ B. $\frac{1}{2 \sqrt{3}} \log \left|\frac{\sqrt{3}+\cos x}{\sqrt{3}-\cos x}\right|+C$ C. $\frac{1}{2 \sqrt{3}} \log \left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(4 \sin ^{2} x+5 \cos ^{2} x\right)}=?$ A. $\frac{1}{2} \tan ^{-1}\left(\frac{\tan x}{\sqrt{5}}\right)+C$ B. $\frac{1}{\sqrt{5}} \tan ^{-1}\left(\frac{\tan x}{\sqrt{5}}\right)+C$ C. $\frac{1}{2 \sqrt{5}} \tan ^{-1}\left(\frac{2 \tan x}{\sqrt{5}}\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(\sin ^{2} x-4 \cos ^{2} x\right)}=?$ A. $\frac{1}{4} \log \left|\frac{\tan x-2}{\tan x+2}\right|+C$ B. $\frac{1}{4} \log \left|\frac{\tan x+2}{\tan x-2}\right|+C$ C. $\frac{1}{4} \log \left|\frac{1-\tan x}{1+\tan x}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x}{\left(x^{4}-16\right)} d x=?$ A. $\frac{1}{4} \log \left|\frac{x^{2}+4}{x^{2}-4}\right|+C$ B. $\frac{1}{16} \log \left|\frac{x^{2}+4}{x^{2}-4}\right|+C$ C. $\frac{1}{16} \log \left|\frac{x^{2}-4}{x^{2}+4}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(4 \mathrm{x}^{2}-1\right)}=?$ A. $\frac{1}{2} \log \left|\frac{2 x-1}{2 x+1}\right|+C$ B. $\frac{1}{2} \log \left|\frac{2 \mathrm{x}+1}{2 \mathrm{x}-1}\right|+\mathrm{C}$ C. $\frac{1}{4} \log \left|\frac{2 x-1}{2 x+1}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\operatorname{cosec}^{2} x}{\left(1-\cot ^{2} x\right)} d x=?$ A. $\frac{1}{2} \log \left|\frac{1+\cot x}{1-\cot x}\right|+C$ B. $-\frac{1}{2} \log \left|\frac{1+\cot x}{1-\cot x}\right|+C$ C. $\frac{1}{2} \log \left|\frac{1-\cot x}{1+\cot x}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(\cos ^{2} x-3 \sin ^{2} x\right)}=?$ A. $\frac{1}{\sqrt{3}} \log \left|\frac{\sqrt{3}+\tan x}{\sqrt{3}-\tan x}\right|+C$ B. $\frac{1}{\sqrt{3}} \log \left|\frac{1-\sqrt{3} \tan x}{1+\sqrt{3} \tan x}\right|+C$ C. $\frac{1}{2 \sqrt{3}} \log \left|\frac{1+\sqrt{3} \tan x}{1-\sqrt{3} \tan x}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(3-2 \mathrm{x}-\mathrm{x}^{2}\right)}=?$ A. $\frac{1}{4} \log \left|\frac{3+x}{3-x}\right|+C$ B. $\frac{1}{4} \log \left|\frac{1+x}{1-x}\right|+C$ C. $\frac{1}{4} \log \left|\frac{3+x}{1-x}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{x^{2}}{\left(a^{6}-x^{6}\right)} d x=?$ A. $\frac{1}{3 a^{3}} \log \left|\frac{a^{3}+x^{3}}{a^{3}-x^{3}}\right|+C$ B. $\frac{1}{6 a^{3}} \log \left|\frac{a^{3}+x^{3}}{a^{3}-x^{3}}\right|+C$ C. $\frac{1}{6 a^{3}} \log \left|\frac{a^{3}-x^{3}}{a^{3}+x^{3}}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{x}{\left(1-x^{4}\right)} d x=?$ A. $\frac{1}{4} \log \left|\frac{1+x^{2}}{1-x^{2}}\right|+C$ B. $\frac{1}{4} \log \left|\frac{1-x^{2}}{1+x^{2}}\right|+C$ C. $\frac{1}{2} \log \left|\frac{1+x^{2}}{1-x^{2}}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x^{2}}{\left(1-x^{6}\right)} d x=?$ A. $\frac{1}{6} \log \left|\frac{1+x^{3}}{1-x^{3}}\right|+C$ B. $\frac{1}{6} \log \left|\frac{1-x^{3}}{1+x^{3}}\right|+C$ C. $\frac{1}{3} \log \left|\frac{1-x^{3}}{1+x^{3}}\right|+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)})$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(16-4 \mathrm{x}^{2}\right)}=?$ A. $\frac{1}{8} \log \left|\frac{2-x}{2+x}\right|+C$ B. $\frac{1}{16} \log \left|\frac{2-x}{2+x}\right|+C$ C. $\frac{1}{8} \log \left|\frac{2+x}{2-x}\right|+C$ D. $\frac{1}{16} \log \left|\frac{2+x}{2-x}\right|+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(1-9 x^{2}\right)}=?$ A. $\frac{1}{3} \log \left|\frac{1+3 x}{1-3 x}\right|+C$ B. $\frac{1}{3} \log \left|\frac{1-3 x}{1+3 x}\right|+C$ C. $\frac{1}{6} \log \left|\frac{1+3 x}{1-3 x}\right|+C$ D. $\frac{1}{6} \log \left|\frac{1-3 x}{1+3 x}\right|+C$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin 2 x}{\left(\sin ^{4} x+\cos ^{4} x\right)} d x=?$ A. $\tan ^{-1}\left(\tan ^{2} x\right)+C$ B. $x^{2}+C$ C. $-\tan -1\left(\tan ^{2} x\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\left(x^{2}+1\right)}{\left(x^{4}+x^{2}+1\right)} d x=?$ A. $\tan ^{-1} \frac{\left(x^{2}-1\right)}{\sqrt{3}}+C$ $B .$$\frac{1}{\sqrt{3}} \tan ^{-1} \frac{\left(x^{2}-1\right)}{\sqrt{3}}+C$ C $\frac{1}{\sqrt{3}} \tan ^{-1} \frac{\left(x^{2}-1\right)}{\sqrt{3} x}+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(\sin ^{4} x+\cos ^{4} x\right)}=?$ A. $\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\tan ^{2} x-1}{\sqrt{2} \tan x}\right)+C$ B. $\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{\tan ^{2} x-1}{\tan x}\right)+C$ C. $\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{1}{\sqrt{2} \tan x}\right)+C$ D. None of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(4 \mathrm{x}^{2}-4 \mathrm{x}+3\right)}=?$ A. $\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{2 \mathrm{x}-1}{\sqrt{2}}\right)+\mathrm{C}$ B. $\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{2 \mathrm{x}-1}{\sqrt{2}}\right)+\mathrm{C}$ C. $-\frac{1}{\sqrt{2}} \tan ^{-1}\left(\frac{2 \mathrm{x}-1}{\sqrt{2}}\right)+\mathrm{C}$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{d x}{\left(4+9 x^{2}\right)}=?$ A. $\frac{2}{3} \tan ^{-1} \frac{3 x}{2}+C$ B. $\frac{1}{6} \tan ^{-1} 3 x+C$ C. $\frac{1}{6} \tan ^{-1} \frac{3 x}{2}+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{\left(x^{2}-1\right)}{\left(x^{2}+4\right)} d x=?$ A. $x-5 \tan ^{-1} \frac{x}{2}+C$ B. $x-\frac{5}{2} \tan ^{-1} \frac{x}{2}+C$ C. $x-\frac{5}{2} \tan ^{-1} \frac{5 x}{2}+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{x^{2}}{\left(9+4 x^{2}\right)}=?$ A. $\frac{x}{4}-\frac{1}{8} \tan ^{-1} \frac{x}{3}+C$ B. $\frac{x}{4}-\frac{3}{8} \tan ^{-1} \frac{x}{3}+C$ C. $\frac{x}{4}-\frac{3}{8} \tan ^{-1} \frac{2 x}{3}+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(\mathrm{e}^{\mathrm{x}}+\mathrm{e}^{-x}\right)}=?$ A. $\tan ^{-1}\left(\mathrm{e}^{\mathrm{x}}\right)+\mathrm{C}$ B. $\tan ^{-1}\left(\mathrm{e}^{-\mathrm{x}}\right)+\mathrm{C}$ C. $-\tan ^{-1}\left(e^{-x}\right)+C$ D. none of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\mathrm{dx}}{\left(2 \mathrm{x}^{2}+\mathrm{x}+3\right)}=?$ A. $\frac{1}{\sqrt{23}} \tan ^{-1}\left(\frac{4 \mathrm{x}+1}{\sqrt{23}}\right)+\mathrm{C}$ B. $\frac{1}{\sqrt{23}} \tan ^{-1}\left(\frac{\mathrm{x}+1}{\sqrt{23}}\right)+\mathrm{C}$ C. $\frac{2}{\sqrt{23}} \tan ^{-1}\left(\frac{4 \mathrm{x}+1}{\sqrt{23}}\right)+\mathrm{C}$ D. none of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \frac{d x}{\left(x^{2}+4 x+8\right)}=?$ A. $\frac{1}{2} \tan ^{-1}\left(\frac{\mathrm{x}+1}{2}\right)+\mathrm{C}$ B. $\frac{1}{2} \tan ^{-1}\left(\frac{\mathrm{x}+2}{2}\right)+\mathrm{C}$ C. $\frac{1}{2} \tan ^{-1}(\mathrm{x}+2)+\mathrm{C}$ D. $\tan ^{-1}\left(\frac{\mathrm{x}+2}{2}\right)+\mathrm{C}$ Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{2 x^{3}}{\left(4+x^{8}\right)} d x=?$ A. $\frac{1}{2} \tan ^{-1} \frac{x^{4}}{2}+C$ B. $\frac{1}{4} \tan ^{-1} \frac{x^{4}}{2}+C$ C. $\frac{1}{2} \tan ^{-1} x^{4}+C$ D. none of these Solution:...
Read More →