The value of $\int \frac{a^{\sqrt{x}}}{\sqrt{x}}dx$ is equal to

Important Questions on Indefinite Integration

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 85

The value of $\int 5^{5^{5^x}}·5^{5^x}·5^{x}dx$ is equal to

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 86

The value of $\int \frac{\sqrt{\tan x}}{\sin x\cos x}dx$ is equal to

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 87

If $\int \frac{2^x}{\sqrt{1-4^x}}dx=K{\sin }^{-1}\left(2^x\right)+C$, then the value of $K$ is equal to

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 88

If $y=\int \frac{dx}{{\left(1+x^2\right)}^{{\displaystyle \frac{3}{2}}}}$ and $y=0$ when $x=0$, then the value of $y$ when $x=1$ is

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 89

The value of $\int {\tan }^{3}2x\sec 2xdx$ is equal to

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 90

If $\int x^{\frac{13}{2}}·{\left(1+x^{\frac{5}{2}}\right)}^{\frac{1}{2}}dx=P{\left(1+x^{\frac{5}{2}}\right)}^{\frac{7}{2}}+Q{\left(1+x^{\frac{5}{2}}\right)}^{{}^{\frac{5}{2}}}+R{\left(1+x^{{}^{\frac{5}{2}}}\right)}^{\frac{3}{2}}+C,$ then $P, Q$ and $R$ are

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 91

The value of $\int \frac{1-x^7}{x\left(1+x^7\right)}dx$ is equal to

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 29 - Indefinite Integration>Exercise-1>Q 93

The value of $\int e^{{\tan }^{-1}x}\left(\frac{1+x+x^2}{1+x^2}\right)dx$ is equal to