Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{x^{3}}{\left(1+x^{8}\right)} d x=?$ A. $\tan ^{-1} \mathrm{x}^{4}+\mathrm{C}$ B. $4 \tan ^{-1} x^{4}+C$ C. $\frac{1}{4} \tan ^{-1} \mathrm{x}^{4}+\mathrm{C}$ 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: $\int \frac{1}{x^{2}} e^{-1 / x} d x=?$ A. $\mathrm{e}^{-1 / \mathrm{x}}+\mathrm{C}$ B. $-\mathrm{e}^{-1 / \mathrm{x}}+\mathrm{C}$ C. $\frac{e^{-1 / x}}{x}+C$ 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: $\int \sqrt{\frac{1+x}{1-x}} d x=?$ A. $\sin ^{-1} x+\sqrt{1-x^{2}}+C$ B. $\sin ^{-1} x+\left(1+x^{2}\right)+C$ C. $\sin ^{-1} x-\sqrt{1-x^{2}}+C$ 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: $\int \frac{\tan x}{(\sec x+\cos x)} d x=?$ A. $\tan ^{-1}(\cos x)+C$ B. $-\tan ^{-1}(\cos x)+C$ C. $\cot ^{-1}(\cos x)+C$ 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: $\int \frac{(1+\sin x)}{(1+\cos x)} d x=?$ A. $\tan \frac{x}{2}+2 \log \left|\cos \frac{x}{2}\right|+C$ B. $-\tan \frac{x}{2}+2 \log \left|\cos \frac{x}{2}\right|+C$ C. $\tan \frac{x}{2}-2 \log \left|\cos \frac{x}{2}\right|+C$ 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: $\int \operatorname{cosec} x d x=?$ A. $\log |\operatorname{cosec} x-\cot x|+C$ B. $-\log |\operatorname{cosec} x-\cot x|+C$ C. $\log |\operatorname{cosec} x+\cot x|+C$ 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: $\int \sec x d x=?$ A. $\log |\sec x-\tan x|+C$ B. $-\log |\sec x+\tan x|+C$ C. $\log |\sec x+\tan x|+C$ 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: $\int \tan \mathrm{x} \mathrm{dx}=?$ A. $\log |\cos x|+C$ B. $-\log |\cos x|+C$ C. $\log |\sin x|+C$ D. $-\log |\sin x|+C$ 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: $\int \frac{d x}{\{\sqrt{2 x+3}+\sqrt{2 x+3}\}}=?$ A. $\frac{1}{18}(2 x+3)^{3 / 2}+\frac{1}{18}(2 x-3)^{3 / 2}+C$ B. $\frac{1}{18}(2 \mathrm{x}+3)^{3 / 2}-\frac{1}{18}(2 \mathrm{x}-3)^{3 / 2}+\mathrm{C}$ C. $\frac{1}{12}(2 x+3)^{3 / 2}-\frac{1}{12}(2 x-3)^{3 / 2}+C$ 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: $\int\left\{(2 x+1) \sqrt{x^{2}+x+1}\right\} d x=?$ A. $\frac{3}{2}\left(x^{2}+x+1\right)^{3 / 2}+C$ B. $\frac{2}{3}\left(x^{2}+x+1\right)^{3 / 2}+C$ C. $\frac{3}{2}(2 x+1)^{3 / 2}+C$ 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: $\int \frac{d x}{x \sqrt{x^{6}-1}}=?$ A. $\frac{1}{3} \sec ^{-1} x^{3}+C$ B. $\frac{1}{3} \operatorname{cosec}^{-1} \mathrm{x}^{3}+\mathrm{C}$ C. $\frac{1}{3} \cot ^{-1} \mathrm{x}^{3}+\mathrm{C}$ 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: $\int \frac{3 x^{2}}{\left(1+x^{6}\right)} d x=?$ A. $\sin ^{-1} x^{3}+C$ B. $\cos ^{-1} x^{3}+C$ C. $\tan ^{-1} x^{3}+C$ D. $\cot ^{-1} \mathrm{x}^{3}+\mathrm{C}$ 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: $\int \frac{(1+\tan x)}{(1-\tan x)} d x=?$ A. $-\log |\cos x-\sin x|+C$ B. $\log |\cos x-\sin x|+C$ C. $\log |\cos x+\sin x|+C$ 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: $\int \frac{1}{(\sqrt{x+3}-\sqrt{x+2})} d x=?$ A. $\frac{2}{3}(\mathrm{x}+3)^{3 / 2}-\frac{2}{3}(\mathrm{x}+3)^{3 / 2}+\mathrm{C}$ B. $\frac{2}{3}(x+3)^{3 / 2}+\frac{2}{3}(x+3)^{3 / 2}+C$ C. $\frac{3}{2}(x+3)^{3 / 2}-\frac{3}{2}(x+3)^{3 / 2}+C$ 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: $\int \frac{\sin (x-\alpha)}{\sin (x+\alpha)} d x=?$ A. $x \cos 2 \alpha-\sin 2 \alpha \cdot \log |\sin (x+\alpha)|+C$ B. $x \cos 2 \alpha+\sin 2 \alpha \cdot \log |\sin (x+\alpha)|+C$ C. $x \cos 2 \alpha+\sin \alpha \cdot \log |\sin (x+\alpha)|+C$ 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: $\int \frac{x^{4}}{\left(1+x^{2}\right)} d x=?$ A. $\frac{x^{3}}{3}+x+\tan ^{-1} x+C$ B. $\frac{-\mathrm{x}^{3}}{3}+\mathrm{x}-\tan ^{-1} \mathrm{x}+\mathrm{C}$ C. $\frac{x^{3}}{3}-x+\tan ^{-1} x+C$ 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: $\int \frac{(1+\sin x)}{(1-\sin x)} d x=?$ A. $2 \tan x+x-2 \sec x+C$ B. $2 \tan \mathrm{x}-\mathrm{x}+2 \sec \mathrm{x}+\mathrm{C}$ C. $2 \tan x-x-2 \sec x+C$ 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: $\int \tan ^{-1}(\sec x+\tan x) d x=?$ A. $\frac{\pi x}{4}+\frac{x^{2}}{4}+C$ B. $\frac{\pi x}{4}-\frac{x^{2}}{4}+C$ C. $\frac{1}{\left(1+x^{2}\right)}+C$ 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: $\int \tan ^{-1}\left\{\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\right\} d x=?$ A. $2 \mathrm{x}^{2}+\mathrm{C}$ B. $\frac{\mathrm{x}^{2}}{2}+\mathrm{C}$ C. $\frac{2}{\left(1+x^{2}\right)}+C$ 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: $\int \frac{(\cos 2 x-\cos 2 \alpha)}{(\cos x-\cos \alpha)} d x=?$ A. $\sin x+x \cos \alpha+C$ B. $2 \sin x+x \cos \alpha+C$ C. $2 \sin x+2 x \cos \alpha+C$ 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: $\int \frac{\cos 2 x}{\cos ^{2} x \sin ^{2} x} d x=?$ A. $\cot x+\tan x+C$ B. $-\cot x+\tan x+C$ C. $\cot x-\tan x+C$ D. $-\cot x-\tan x+C$ 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: $\int \frac{1}{\sin ^{2} x \cos ^{2} x} d x=?$ A. $\tan x+\cot x+C$ B. $\tan x-\cot x+C$ C. $-\tan x+\cot x+C$ D. none of these Solution: Given...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(1+\cos x)}{(1-\cos x)} d x=?$ A. $-2 \cot \frac{x}{2}-x+C$ B. $-2 \cot \frac{x}{2}+x+C$ C. $2 \cot \frac{x}{2}+x+C$ 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: $\int \frac{(1-\cos 2 x)}{(1+\cos 2 x)} d x=?$ A. $\tan x+x+C$ B. $\tan x-x+C$ C. $-\tan x+x+C$ 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: $\int \sec ^{2} x \operatorname{cosec}^{2} x d x=?$ A. $\tan x-\cot x+C$ B. $\tan x+\cot x+C$ C. $-\tan x+\cot x+C$ D. none of these Solution:...
Read More →