Integrals Test ...

$$\displaystyle\int_0^\pi \frac{1}{1\, +\,\sin x}\ dx$$ is equal to

If $$\quad f(x)=\begin{cases} 2{ x }^{ 2 }+1,x\le 1 \\ 4{ x }^{ 2 }-1,x>1 \end{cases}$$, then $$\int _{ 0 }^{ 2 }{ f(x)dx } $$ is

$$\displaystyle \int \frac{\sin 2x}{\sin^2x+2 \cos^2x}dx=$$

If $$\displaystyle \int_{0}^{b} \displaystyle \frac{dx}{1\, +\, x^2}\, =\, \displaystyle \int_{b}^{\infty} \displaystyle \frac{dx}{1\, +\, x^2}$$, then $$b = $$

$$\displaystyle \int{\tan^2x}dx$$

The value of $$I=\displaystyle \int _{ 0 }^{ \frac { \pi  }{ 4 }  }{ \left( \tan ^{ n+1 }{ x }  \right) dx } +\frac { 1 }{ 2 } \int _{ 0 }^{ \frac { \pi  }{ 2 }  }{ \left( \tan ^{ n+1 }{ \left( \frac { x }{ 2 }  \right)  }  \right) dx } $$ is

$$\displaystyle \int (1 + x - x^{-1})e^{x + x^{-1}}dx$$ is equal to

What is $$\displaystyle \int _{ 0 }^{ 1 }{ \cfrac { \tan ^{ -1 }{ x }  }{ 1+{ x }^{ 2 } }  } dx$$ equal to?

$$\displaystyle\int^{\pi /2}_{-\pi /2}\cos x$$ ln $$\left(\displaystyle\frac{1+x}{1-x}\right)dx$$ is equal to.

What is $$\displaystyle\int _{ 1 }^{ 2 }{ \ln { x } dx } $$ equal to?