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

Important Questions on Indefinite Integration

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 17

$\int \frac{dx}{\left(1+\sqrt{x}\right)\sqrt{x-x^2}}$ is equal to

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 18

Let $f^{\text{'}}\left(x\right)=3x^2·\sin \frac{1}{x}-x\cos \frac{1}{x},x\ne 0,f\left(0\right)=0,f\left(\frac{1}{\pi }\right)=0$, then which of the following is/are not correct.

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 19

$\int \frac{1}{x^2-1}\ln \frac{x-1}{x+1}dx$ equals -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 20

$\int \frac{dx}{\sqrt{x-x^2}}$ equals, where $x\in \left(\frac{1}{2},1\right)$ -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 21

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

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 22

Primitive of $\sqrt{1+2 \tan x\left(\sec x+\tan x\right)}$ w.r.t.$x$ is

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 23

$\int \sin 2xdx$ equals -

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 24

$\int \frac{dx}{x^3\left(1-\frac{1}{2x^2}\right)}$ equals -