Integrals Test ...

$$\displaystyle\int^{\lambda}_0\dfrac{y}{\sqrt{y+\lambda}}dy=?$$

The integral $$\int { \dfrac { { sin }^{ 2 }\times { cos }^{ 2 }\times  }{ { (sin }^{ 5 }\times +{ cos }^{ 3 }\times { sin }^{ 2 }\times +{ sin }^{ 3 }\times { cos }^{ 2 }\times +{ cos }^{ 5 }{ \times ) }^{ 2 } }  } $$dx is equal to:

$$\int_{1}^{\infty }(e^{x+1}+e^{3-x})^{-1}dx$$ is equal to: 

The value of the integral $$\displaystyle \int _{ { e }^{ -1 } }^{ { e }^{ 2 } }{ \left| \frac { \log _{ e }{ x }  }{ x }  \right| dx } $$ is

The value of the integral $$\displaystyle \int _ { 0 } ^ { 1 } \dfrac { d x } { x ^ { 2 } + 2 x \cos \alpha + 1 }$$ , where $$0 < \alpha < \dfrac { \pi } { 2 } ,$$ is equal to

$$\displaystyle \int _ { 0 } ^ { \pi / 4 } \frac { x \cdot \sin x } { \cos ^ { 3 } x } d x$$ equals to :

$$\int_{0}^{\frac{1}{2}}\frac{xsin^{-1}x}{\sqrt{1-x^{2}}}dx$$ is equal to

Value of the definite integral $$\displaystyle \int_{-1}^{1}\dfrac {dx}{(1+x^{3}+\sqrt {1+x^{6}})}$$

If $$f(x)=\begin{vmatrix} \cos { x }  & 1 & 0 \\ 1 & 2\cos { x }  & 1 \\ 0 & 1 & 2\cos { x }  \end{vmatrix}$$ then $$\displaystyle\int _{ 0 }^{ \pi /2 }{ f\left( x \right) } dx$$ is equal to 

The value of $$\int_{0}^{[x]} (x-[x])dx$$, where $$[x]$$ is the greatest integer $$|le x$$ is equal to