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

If $I=\int \frac{2}{x}\left(x^{\ln x}\right){\left(\ln x\right)}^{3}dx=A{x}^{\ln x}{\left(\ln x\right)}^2-B{x}^{\ln x}+C,$ then $\frac{A}{B}$ is equal to:

If $I_n=\int {\left(\sin x+\cos x\right)}^{n}dx, n\in N, n\ge 2$ and $I_n=\frac{1}{n}{\left(\sin x+\cos x\right)}^{n-1}\left(\sin x-\cos x\right)+\frac{2k}{n}{I}_{n-2}$, then $k=$

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

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

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?

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

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

If $\frac{C_0}{1}+\frac{C_1}{2}+\frac{C_2}{3}=0,$ where $C_0, C_1, C_2$ are all real, the equation $C_2{x}^2+C_{1}x+C_0=0$ has