If $\int \frac{x^2-x+1}{{\left(1+x^2\right)}^{{\displaystyle \frac{3}{2}}}}{e}^{x}dx=e^{x}f\left(x\right)+C$, then

Important Questions on Indefinite Integration

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 48

If $\int \frac{4e^x+6e^{-x}}{9e^x-4e^{-x}}dx=Ax+B \ln \left|9e^{2x}-4\right|+C,$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 49

The value of $\int \frac{x^2+{\cos }^{2}x}{1+x^2}{cosec}^{2}xdx$ is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 50

The value of $\int \frac{dx}{\sqrt{x-x^2}}; \left(x>\frac{1}{2}\right)$ is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 51

$\int \frac{x^3-1}{x^3+x}dx$ is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 52

The value of $2\int \sin xcosec4xdx$ is equal to

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 53

If $\int \frac{3\cot 3x-\cot x}{\tan x-3\tan 3x}dx=pf\left(x\right)+qg\left(x\right)+C$, then which of the following may be correct?

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 54

If $\int \frac{dx}{5+4\cos x}=P{\tan }^{-1}\left(m\tan \frac{x}{2}\right)+C$, then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-2>Q 55

The value of $\int \frac{\sin 2x}{{\sin }^{4}x+{\cos }^{4}x}dx$ is equal to