Integrals Test ...

$$\int _{ 0 }^{ 1 }{ \dfrac { dx }{ \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+2 \right)  }  } $$=

$$\int \left( x ^ { 6 } + 7 x ^ { 5 } + 6 x ^ { 4 } + 5 x ^ { 3 } + 4 x ^ { 2 } + 3 x + 1 \right) e ^ { x } d x$$ equals

Evaluate$$\displaystyle \int _ { 0 } ^ { a } \dfrac { x d x } { \sqrt { a ^ { 2 } + x ^ { 2 } } } $$

Evaluate $$\displaystyle \int _ { 0 } ^ { \infty } \frac { x ^ { 2 } + 1 } { x ^ { 4 } + 7 x ^ { 2 } + 1 } d x $$

The intercepts on x-axis made by tangents to the curve, $$\int _{ 0 }^{ x }{ \left| t \right|  } dt,x\in R,$$ which are parallel to the line y=2x, are equal to:

$$\int _{ 0 }^{ \pi  }{ \cfrac { { x }^{ 2 } }{ { \left( 1+sinx \right)  }^{ 2 } }  } dx$$ equals

The value of $$\int _{ -1 }^{ 1 }{ \dfrac { { cot }^{ -1 }x }{ \pi  }  } dx$$

The value of the integral $$\displaystyle \int_{-\pi/2}^{\pi/2} \left(x^{2}+\log \dfrac{\pi-x}{\pi+x}\right) \cos x dx $$ is 

If $$\int \frac { x ^ { 2 } \tan ^ { - 1 } x } { 1 + x ^ { 2 } } d x = \tan ^ { - 1 } x - \frac { 1 } { 2 } \log \left( 1 + x ^ { 2 } \right) + f ( x ) + c$$ then $$f ( x ) =$$

$$\begin{matrix} lim \\ n\rightarrow \infty  \end{matrix}\int _{ 0 }^{ 1 }{ \frac { { nx }^{ { n- }1 } }{ { 1+x }^{ 2 } } dx= } $$