Embibe Experts Solutions for Exercise 6: Assignment Set-2

$\int \frac{\sqrt{1+x^2}}{1-x^2}dx=-\frac{\sqrt{2}}{2}\ln \left|f\left(x\right)\right|+g\left(x\right)+c$, then $f\left(x\right)$ and $g\left(x\right)$ are

If $\int \frac{dx}{e^{2x}+e^{-2x}}=\frac{A}{842}{\tan }^{-1}{e}^{2x}+c$ then $A$ equals.....

Evaluate $\int \frac{a+b\sin x}{(b+a\sin x{)}^2}dx$

If $\int \frac{dx}{x+x^{2021}}=f\left(x\right)+c$ and $\lambda =f\left((e-1{)}^{\frac{-1}{2020}}\right)$ then $\frac{-1}{\lambda }$ is equal to

If $\int \frac{(2x+5)dx}{x(x+2)(x+3)(x+5)}=\frac{1}{n}\ln \left[\frac{x^2+px}{x^2+px+q}\right]+c$ where $n,p,q\in N$ then $n+p+q$ is equal to

If $\int {\cos }^{n}xdx=\frac{{\cos }^{n-1}x·\sin x}{n}+f\left(n\right)\int {\cos }^{n-2}xdx$, then $5+f\left(100\right)$ is equal to

If $f\left(x\right)=\int x^x(1+\ln x)dx$ then the value of $f\left(5\right)-f\left(3\right)$ is equal to

If $\int \frac{\sin x+{\sin }^{3}x}{\cos 2x}dx=A\cos x+B \mathrm{In} \left|\frac{\sqrt{2}\mathrm{cosx}+1}{\sqrt{2}\mathrm{cosx}-1}\right|+\mathrm{c}$ then value of $\left(A^{-1}+9B^{-2}\right)$ is equal to