Primitive of $\frac{3x^4-1}{{\left(x^4+x+1\right)}^2}$ w.r.t. $x$ is -

Important Questions on Indefinite Integration

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 12

$\int \frac{dx}{x^4{\left[x\left(x^5-1\right)\right]}^{1/3}}$ equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 13

$\int \frac{\sin x}{\sin 4x}dx$ is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 14

The value of integral $\int \frac{d\theta }{{\cos }^3\theta \sqrt{\sin 2\theta }}$ can be expressed as irrational function of $\tan \theta$ as

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 15

If $\int \frac{3\sin x+2\cos x}{3\cos x+2\sin x}dx=ax+b \ln \left|2\sin x+3\cos x\right|+c$, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 16

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

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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

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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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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 -