Embibe Experts Solutions for Chapter: Indefinite Integration, Exercise 2: EXERCISE-2

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

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 -

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.

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

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

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

$\int \sin 2xdx$ equals -

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