Integrals Test ...

$$\displaystyle \int_{-1}^{3}\left( \tan^{ -1 }\frac { x }{ x^{ 2 }+1 } +\tan ^{ -1 } \frac { x^{ 2 }+1 }{ x }  \right) dx=$$

If $$\displaystyle \int_{1/\sqrt{3}}^{k}\dfrac{1}{1+x^{2}}dx=$$ $$\dfrac{\pi}{6}$$ 

$$\displaystyle \int_{0}^{1}\frac{4x^{3}}{\sqrt{1-x^{8}}}dx =?$$

The integral $$\displaystyle \int_{0}^{\pi/4}\frac{\sin^{9}x}{\cos^{11}x}dx=$$

$$\displaystyle \int_{0}^{\pi_/{2}}\frac{\cos x}{1+\sin x}d_{X=}$$

Evaluate: $$\displaystyle \int_{0}^{1}\frac{\tan^{-1}x}{1+x^{2}}dx$$

Evaluate: $$\displaystyle \int_{1}^{2}\frac{1}{x\sqrt{x^{2}-1}}d{x}$$

The value of $$\int_{0}^{\infty} x.e^{-x^{2}}dx_{=}$$

$$\displaystyle \int_{0}^{1}\frac{x^{2}}{1+x^{2}}dx$$ equals

$$\displaystyle \int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}=$$