Integrals Test ...

$$\displaystyle \int _{ 0 }^{ { \pi  }^{ 2 } }{ \dfrac { \sin { \sqrt { x }  }  }{ \sqrt { x }  }  }  dx$$ is equal to

The integral $$\int _{ 2a/4 }^{ a/2 }{ (2\quad cosecx{ ) }^{ 17 } } $$ dx is equal to:

Solve : $$\int^1_{0^+} \dfrac{x^x(x^{2x} +1)(lnx +1)}{x^{4x}+1} dx$$

$$\displaystyle \int \frac { e ^ { x } ( 1 + \sin x ) } { 1 + \cos x } d x =$$

The value of the integral $$\int _{ 0 }^{ 1 }{ \sqrt { \frac { 1-x }{ 1+x }  }  } $$ dx is

Let $$A = \int _ { 0 } ^ { 1 } \frac { e ^ { t } } { t + 1 }$$ dt,  then the value of $$\int _ { 0 } ^ { 1 } \frac { t e ^ { t ^ { 2 } } } { t ^ { 2 } + 1 } d t$$ is:-

The value of the integral $$\int _{ -\pi /2 }^{ \pi /2 }{ \left[ { x }^{ 2 }+log\frac { \pi -x }{ \pi +x }  \right]  } $$ cos x dx is 

$$\int _ { 0 } ^ { 1 } \frac { d x } { \sqrt { x + 1 } + \sqrt { x } } d x =$$

The value of the integral $$\int _ { - \pi } ^ { \pi } ( \cos p x - \sin q x ) ^ { 2 } d x$$ where $$p , q$$ are integers, is equal to:-

$$\int _{ -1 }^{ 1/2 }{ \dfrac { { e }^{ x }\left( 2-{ x }^{ 2 } \right) dx }{ \left( 1-x \right) \sqrt { 1-{ x }^{ 2 } }  }  } $$ is equal to