K. C. Sinha Solutions for Chapter: Indefinite Integrals - II, Exercise 2: EXERCISE

If$\int f\left(x\right)·\cos x dx=\frac{1}{2}{\left\{f\left(x\right)\right\}}^2+C$, then $f\left(0\right)=$

$\int \left[\frac{1}{\log x}-\frac{1}{(\log x{)}^2}\right]dx=$ (Where $C$ is constant of integration) 

$\int \frac{x{e}^x}{(1+x{)}^2} dx=$ (Where $C$ is constant of integration)

If $\int \frac{\sin x}{\sin \left(x-\alpha \right)}dx=Ax+B\log \left(\sin x-\alpha \right)+C$, then the value of $(A,B)$ is (Where $C$ is constant of integration) 

$\int \frac{dx}{\cos x-\sin x}$ is equal to (Where $C$ is constant of integration)

$\int {\left\{\frac{\log x-1}{1+{\left(\log x\right)}^2}\right\}}^2 dx$ is equal to (Where $C$ is constant of integration)

$\int \frac{dx}{\cos x+\sqrt{3}\sin x}$ equals (Where $C$ is constant of integration)

The value of $\sqrt{2}\int \frac{\sin x dx}{\sin \left(x-{\displaystyle \frac{\pi }{4}}\right)}$ is (Where $C$ is constant of integration)