Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \cot ^{2} x d x=?$ A. $-x \cot x+\frac{x^{2}}{2}+\log |\sin x|+C$ B. $-x \cot x-\frac{x^{2}}{2}+\log |\sin x|+C$ C. $-x \cot x+\frac{x^{2}}{2}-\log |\sin x|+C$ 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: $\int\left(x 2^{x}\right) d x=?$ A. $\frac{2^{x}}{(\log 2)}(x+\log 2)+C$ B. $\frac{2^{x}}{(\log 2)^{2}}(x+\log 2-1)+C$ C. $\frac{x \cdot 2^{x}}{(\log 2)}+\frac{2^{x}}{(\log 2)^{2}}+C$ 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: $\int 2 x^{3} e^{x^{2}} d x=?$ A. $e^{x^{2}}\left(x^{2}-1\right)+C$ B. $\mathrm{e}^{\mathrm{x}^{2}}\left(\mathrm{x}^{2}+1\right)+\mathrm{C}$ C. $e^{x^{2}}(x+1)+C$ 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: $\int\left\{\frac{1}{(\log x)}-\frac{1}{(\log x)^{2}}\right\} d x=?$ A. $\times \log x+C$ $B .$ $\frac{x}{\log x}+C$ 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: $\int \sec ^{3} x d x=?$ A. $\frac{1}{2}\{\sec x \tan x-\log |\sec x+\tan x|\}+C$ B. $\frac{1}{2}\{\sec x \tan x+\log |\sec x+\tan x|\}+C$ C. $2\{\sec x \tan x+\log |\sec x+\tan x|\}+C$ 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: $\int \cos (\log x) d x=?$ A. $\frac{x}{2}[\cos (\log x)-\sin (\log x)]+C$ B. $\frac{x}{2}[\cos (\log x)+\sin (\log x)]+C$ C. $2 x[\cos (\log x)+\sin (\log x)]+C$ D. $2 x[\cos (\log x)-\sin (\log x)]+C$ 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: $\int \cos \sqrt{x} d x=?$ A. $\sin \sqrt{x}+\cos \sqrt{x}+C$ B. $\frac{1}{2}(\sqrt{x} \sin \sqrt{x}-\cos \sqrt{x})+C$ C. $2[\sqrt{\mathrm{x}} \sin \sqrt{\mathrm{x}}+\cos \sqrt{\mathrm{x}}]+\mathrm{C}$ 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: $\int \mathrm{e}^{\sqrt{x}} \mathrm{dx}=?$ A. $e^{\sqrt{x}}+\sqrt{x}+C$ B. $\frac{1}{2} e^{\sqrt{x}}(\sqrt{x}+1)+C$ C. $2 e^{\sqrt{x}}(\sqrt{x}-1)+C$ 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: $\int(\log x)^{2} \mathrm{dx}=?$ A. $\frac{2 \log x}{x}+C$. B. $\frac{1}{3}(\log x)^{3}+C$ C. $x(\log x)^{2}-2 x \log x+2 x+C$ D. $x(\log x)^{2}+2 x \log x-2 x+C$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \log _{10} \mathrm{xdx}=?$ A. $\frac{1}{\mathrm{x}} \log _{\mathrm{e}} 10+\mathrm{C}$ B. $\frac{1}{\mathrm{x}} \log _{10} \mathrm{e}+\mathrm{C}$ C. $x(\log x-1) \log _{e} 10+C$ D. $x(\log x-1) \log _{10} e+C$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \log x d x=?$ A. $\frac{1}{\mathrm{x}}+\mathrm{C}$ B. $\frac{1}{2}(\log x)^{2}+C$ C. $x(\log x+1)+C$ D. $x(\log x-1)+C$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\log x}{x^{2}} d x=?$ A. $-\frac{1}{x}(\log x+1)+C$ B. $\frac{1}{x}(\log x-1)+C$ C. $\frac{1}{\mathrm{x}}(\log \mathrm{x}+1)+\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \cos ^{2} x d x=?$ A. $\frac{x^{2}}{4}-\frac{x \sin 2 x}{4}+\frac{\cos 2 x}{8}+C$ B. $\frac{x^{2}}{4}+\frac{x \sin 2 x}{4}+\frac{\cos 2 x}{8}+C$ C. $\frac{x^{2}}{4}+\frac{x \sin 2 x}{4}-\frac{\cos 2 x}{8}+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \sin x \cos x d x=?$ A. $-\frac{1}{4} x \sin 2 x+\frac{1}{8} \cos 2 x+C$ B. $\frac{1}{4} x \cos 2 x-\frac{1}{8} \sin 2 x+C$ C. $\frac{1}{2} \mathrm{x} \sin 2 \mathrm{x}+\frac{1}{4} \cos 2 \mathrm{x}+\mathrm{C}$ D. $-\frac{1}{4} x \cos 2 x+\frac{1}{8} \sin 2 x+C$ 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: $\int x \operatorname{cosec}^{2} x d x=?$ A. $x \cot x-\log |\sin x|+C$ B. $-\cot x+\log |\sin x|+C$ C. $x \tan x-\log |\sec x|+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int x \log x d x=?$ A. $x \log x+\frac{1}{2} x^{2}+C$ B. $\frac{1}{2} x^{2} \log x+\frac{1}{4} x^{2}+C$ C. $\frac{1}{2} x^{2} \log x-\frac{1}{4} x^{2}+C$ 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: $\int x \sin 2 x d x=?$ A. $\frac{1}{2} \mathrm{x} \cos 2 \mathrm{x}+\frac{1}{4} \sin 2 \mathrm{x}+\mathrm{C}$ B. $-\frac{1}{2} x \cos 2 x-\frac{1}{4} \sin 2 x+C$ C. $-\frac{1}{2} x \cos 2 x+\frac{1}{4} \sin 2 x+C$ 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: $\int x \sec ^{2} x d x=?$ A. $x \tan x-\log |\cos x|+C$ B. $x \tan x+\log |\cos x|+C$ C. $x \tan x+\log |\sec x|+C$ 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: $\int x \cos 2 x d x=?$ A. $\frac{1}{2} x \sin 2 x+\frac{1}{4} \cos 2 x+C$ B. $\frac{1}{2} x \sin 2 x-\frac{1}{4} \cos 2 x+C$ C. $2 x \sin 2 x+4 \cos 2 x+C$ 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: $\int x e^{2 x} d x=?$ A. $\frac{1}{2} \mathrm{x} \mathrm{e}^{2 \mathrm{x}}+\frac{1}{4} \mathrm{e}^{2 \mathrm{x}}+\mathrm{C}$ B. $\frac{1}{2} \mathrm{x} \mathrm{e}^{2 \mathrm{x}}-\frac{1}{4} \mathrm{e}^{2 \mathrm{x}}+\mathrm{C}$ C. $2 \mathrm{x} \mathrm{e}^{2 \mathrm{x}}+4 \mathrm{e}^{2 \mathrm{x}}+\mathrm{C}$ 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: $\int x e^{x} d x=?$ A. $e^{x}(1-x)+C$ B. $e^{x}(x-1)+C$ C. $e^{x}(x-1)+C$ D. none of these Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{2 x}\left(\frac{1-\sin 2 x}{1-\cos 2 x}\right) d x$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \mathrm{e}^{2 \mathrm{x}}\left(\frac{1+\sin 2 \mathrm{x}}{1+\cos 2 \mathrm{x}}\right) \mathrm{dx}$ Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int 5^{5^{5 x}} \cdot 5^{5^{x}} \cdot 5^{x} d x$ Solution:...
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Question: Evaluate the following integrals: $\int\left(\frac{\sin ^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\sin ^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}}\right) d x$ Solution:...
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