Integrals Test ...

$$\displaystyle \int_{\frac{5}{2}}^{5}\frac{\sqrt{(25-x^2)^3}}{x^4}\:dx$$ is equal to

$$\displaystyle \int_{0}^{1}\frac{3^{x+1}-4^{x-1}}{12^{x}}dx=$$

The value of $$\int _{-\pi /2}^{\pi /2}\left (psin^3 x+qsin^4 x +r sin^5 x  \right )$$ does not depend on

If $$ \displaystyle \int_{0}^{1} \frac{\tan^{-1} x}{x}dx$$  is equal to

The value of the integral $$\displaystyle \int_{0 }^{\log5}\frac{e^x\sqrt{e^x-1}}{e^x+3}\:dx$$ is

The value of the integral  $$\displaystyle \int_{0}^{\frac{1}{\sqrt{3}}}\frac{dx}{(1+x^2)\sqrt{1-x^2}}$$

Let  $$ \displaystyle I_1=\int_{0}^{1}\frac{e^x dx}{1+x}$$ and $$\displaystyle I_2=\int_{0}^{1}\dfrac{x^2 dx}{e^{x^3}(2-x^3)}$$.

The value of the integral $$\displaystyle \int_{-\pi}^{\pi} (\cos  ax - \sin  b  x)^2 dx$$, where $$a$$ and $$b$$ are integers, is

If $$\displaystyle \int_{1}^{2} e^{x^2} dx= a$$, then $$\displaystyle \int_{e}^{e^4}\sqrt{\ln x} \:dx$$ is equal to

$$\displaystyle \int_{ 0 }^{\infty}\frac{ \:dx}{\left [ x+\sqrt{x^2+1} \right ]^3}$$ is equal to