Integrals Test ...

$$\displaystyle \int_{1}^{2}(\frac{1+x\log x}{x})e^{x}dx_{=}$$

Evaluate the integral
$$\displaystyle \int_{\frac{\sqrt{2}}{3}}^{ \frac{\sqrt{3}}{3}}\displaystyle \frac{dx}{\sqrt{4-9x^{2}}}$$

$$\displaystyle \int_{0}^{\pi /2} \displaystyle \frac{1}{\sin x+\cos x} \ dx $$

Evaluate the integral
$$\displaystyle \int_{0}^{\pi_/{2}}\cos^{5}x.\sin 2xdx$$

$$ \int_{\pi /4}^{\pi /2} Cotx.dx_{=}$$

Evaluate the integral
$$\displaystyle \int_{0}^{1}\frac{dx}{\sqrt{1-x^{2}}}$$

$$\displaystyle \int_{0}^{\displaystyle \tfrac{\pi}{4}}\sqrt{\frac{1-\sin 2x}{1+\sin 2x}}dx=$$

Evaluate the integral
$$\displaystyle \int_{0}^{1}\frac{(\sin^{-1} {x})^{2}}{\sqrt{1-x^{2}}}dx $$

Evaluate the integral
$$\displaystyle \int_{1/2}^{1}\frac{1}{\sqrt{1-x^{2}}}dx$$

$$\displaystyle \int_{0}^{1}\sqrt{1-x^{2}}dx_{=}$$