Integrals Test ...

Evaluate the integral
$$\displaystyle \int_{0}^{\pi/4}\frac{\sin x+\cos x}{3+\sin 2x} dx$$ 

Evaluate: $$\displaystyle \int_{0}^{1}\frac{x^{3}}{1+x^{8}} dx$$ 

The value of $$x$$ such that  $$\displaystyle \int_{\sqrt{2}}^{\mathrm{x}}\frac{1}{x\sqrt{x^{2}-1}}dx=\frac{\pi}{12}$$ is

Evaluate: $$\displaystyle \int_{0}^{\pi/4}\sec^{6}x \ dx$$

lf $$f(x)=\left\{\begin{array}{l}e^{\cos x}\sin x, for |x|\leq 2\\2    ;       otherwise\end{array}\right.$$, then $$\displaystyle \int_{-2}^{3}f(x)dx$$ is

The function $$F(x)=\displaystyle \int_{0}^{x}\log(t+\sqrt{1+t^{2}})dt$$ is

The value of $$\displaystyle \int_{0}^{1}\frac{2^{2x+1}-5^{2x-1}}{10^{x}} dx$$ is

lf $$\displaystyle \int_{0}^{1}\frac{\tan^{-1}x}{x}dx=k\int_{0}^{\pi/2}\frac{x}{\sin x}dx$$, then the value of $$k$$ is

The value of the integral $$\displaystyle \int_{0}^{\infty}\frac{1}{1+x^{4}} dx$$ is

$$\displaystyle \int e^{tan^{-1}x}\left[\frac{1+x+x^{2}}{1+x^{2}}\right]dx=$$