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Question: Evaluate: $\int \frac{x}{\left(1-x^{4}\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{2 x^{3}}{\left(4+x^{8}\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{3 x^{5}}{\left(1+x^{12}\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{\cos x}{\left(1+\sin ^{2} x\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{\sin x}{\left(1+\cos ^{2} x\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{e^{x}}{\left(e^{2 x}+1\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{x^{2}}{\left(9+4 x^{2}\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{\left(x^{2}-1\right)}{\left(x^{2}+4\right)} d x$ Solution:...
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Question: Evaluate: $\int \frac{d x}{\left(16 x^{2}-25\right)}$ Solution:...
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Question: Evaluate: $\int \frac{d x}{\left(50+2 x^{2}\right)}$ Solution:...
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Question: Evaluate: $\int \frac{d x}{\left(4+9 x^{2}\right)}$ Solution:...
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Question: Evaluate: $\int \frac{d x}{\left(x^{2}+16\right)}$ Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}\left(\frac{1+\sin x}{1+\cos x}\right) d x=?$ A. $e^{x} \sin \frac{x}{2}+C$ B. $e^{x} \cos \frac{x}{2}+C$ C. $e^{x} \tan \frac{x}{2}+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int e^{x} \cdot \frac{x}{(1+x)^{2}} d x=?$ A. $\mathrm{e}^{\mathrm{x}} \cdot \frac{1}{(1+\mathrm{x})}+\mathrm{C}$ B. $e^{x} \cdot \frac{1}{x}+C$ C. $e^{x} \cdot \frac{x}{(1+x)}+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}\left(\frac{1+x \log x}{x}\right) d x=?$ A. $e^{x} \cdot \frac{1}{x}+C$ B. $e^{x} \log x+C$ C. $x e^{x} \log x+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x} \sec x(1+\tan x) d x=?$ A. $e^{x}(1+\tan x)+C$ B. $e^{x} \sec x+C$ C. $e^{x} \tan x+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}(\sin x+\cos x) d x=?$ A. $e^{x} \sin x+C$ B. $e^{x} \cos x+C$ C. $e^{x} \tan x+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}\left(\cot x-\operatorname{cosec}^{2} x\right) d x=?$ A. $-e^{x} \operatorname{cosec}^{2} x+C$ B. $e^{x} \cot x+C$ C. $-\mathrm{e}^{\mathrm{x}} \cot \mathrm{x}+\mathrm{C}$ D. None of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int e^{x}(\tan x-\log \cos x) d x=?$ A. $e^{x} \tan x+C$ B. $e^{x} \log \cos x+C$ C. $e^{x} \log \sec x+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}\left\{\tan ^{-1} x+\frac{1}{\left(1+x^{2}\right)}\right\} d x=?$ A. $e^{x} \cdot \frac{1}{\left(1+x^{2}\right)}+C$ B. $e^{x} \tan ^{-1} x+C$ C. $-e^{x} \cot ^{-1} x+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int e^{x}(\cot x+\log \sin x) d x=?$ A. $e^{x} \log (\sec x+\tan x)+C$ B. $e^{x} \sec x+C$ C. $e^{x} \log \tan x+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int e^{x}(\tan x+\log \sec x) d x=?$ A. $e^{x} \log \sec x+C$ B. $e^{x} \tan x+C$ C. $e^{x}(\log \cos x)+C$ D. none of these Solution:...
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