Integrals Test ...

If $$\displaystyle \int_{\log 2}^{x}\frac{1}{\sqrt{e^x-1}}dx=\frac{\pi }{6}$$, then the value of $$x$$ is 

$$\displaystyle\int { \cfrac { 1 }{ 7 } \sin { \left( \cfrac { x }{ 7 } +10 \right)  } dx } $$ is equal to

If $$\displaystyle\int { \sqrt { 1+\sin { x }  } \cdot f\left( x \right) dx } =\dfrac { 2 }{ 3 } { \left( 1+\sin { x }  \right)  }^{ { 3 }/{ 2 } }+C$$, then $$f\left( x \right) $$ is equal to

$$\displaystyle\int { { x }^{ x }\log { \left( ex \right)  } dx } $$ is equal to

$$\displaystyle \int _{ 0 }^{ \pi/2}{ \frac{1}{a + b \cos x}} dx, a > |b| =$$.

$$\displaystyle\int _{ 0 }^{ { \sqrt { \pi  }  }/{ 2 } }{ 2{ x }^{ 3 }\sin { \left( { x }^{ 2 } \right)  } dx } $$ is equal to

If $$ \int _0^1 xdx = \dfrac {\pi}{4} - \dfrac {1}{2} ln 2 $$ then the value of definite integral $$ \int _0^1 \tan^{-1} (1-x+x^2) dx $$ equals :

$$\displaystyle \int_{0}^{\infty} \dfrac {x \ln x}{(1 + x^{2})^{2}}dx =$$

Given $$\int_{1}^{2} e^{x^{2}} dx = a$$ the the value of $$\int_{e}^{e^{4}}\sqrt {ln x} dx$$ is

If $$f\left( x \right) $$ is defined $$\left[ -2,2 \right] $$ by $$f\left( x \right) =4{ x }^{ 2 }-3x+1$$ and $$g\left( x \right) =\dfrac { f\left( -x \right) -f\left( x \right)  }{ { x }^{ 2 }+3 } $$, then $$\displaystyle\int _{ -2 }^{ 2 }{ g\left( x \right) dx } $$ is equal to