Integrals Test ...

If $$\displaystyle I_{1}= \int_{-4}^{-5}e^{\left ( x +5 \right )^{2}}dx$$ and $$\displaystyle I_{2}= 3\int_{{1}/{3}}^{{2}/{3}}e^{\left ( 3x -2 \right )^{2}}dx$$ 

Evaluate the integrals $$\displaystyle \int_{a}^{b}\frac{\log x}{x}dx$$

If $$f\left ( a+x \right )= f\left ( x \right )$$ , then $$\forall$$ $$ a> 0,  n\epsilon  N$$ the value of $$\displaystyle \int_{0}^{n a}f\left ( x \right )dx$$  equals ?

Given $$\displaystyle \int _{ 1 }^{ 2 }{ { e }^{ { x }^{ 2 } } } dx=a,$$ the value of $$\displaystyle \int _{ e }^{ { e }^{ 4 } }{ \sqrt { \ln { \left( x \right)  }  } dx } $$ is?

$$\displaystyle \int_{0}^{\pi /2}\frac{dx}{\sin x}$$equals

The value of $$\displaystyle \int_{0}^{1}\displaystyle \frac{dx}{\left ( x+1 \right )\sqrt{x^{2}+2x}}$$ is

Value of $$\displaystyle \int_{0}^{\pi /4}\left ( \sqrt{\tan x}-\sqrt{\cot x} \right )\: dx$$ is

Value of $$\displaystyle \int_{0}^{2a}\dfrac{x^{3/2}}{\sqrt{2a-x}} dx$$ is

If $$f\left ( x \right )= A\sin \left ( \dfrac {\pi x}{2} \right )\: +\: B,f{}'\left ( \dfrac 12  \right )= \sqrt{2}$$ and $$\displaystyle \int_{0}^{1}f\left ( x \right )dx= \displaystyle \frac{2A}{\pi }$$, 

The value of $$\displaystyle \int_{a}^{b}\displaystyle \frac{\log x}{x}\: dx$$ is