Integrals Test ...

What is $$\displaystyle \int \dfrac{x^4 - 1}{x^2 \sqrt{x^4 + x^2 + 1}} dx$$ equal to?

The value of $$\displaystyle\int _{ 0 }^{ { x }/{ 4 } }{ \dfrac { \sec { x }  }{ { \left( \sec { x } +\tan { x }  \right)  }^{ 2 } } dx } $$ is

What is $$\displaystyle \int_0^1 {\frac{\tan^{-1}x}{1 + x^2} dx}$$ equal to ?

If $$I=\displaystyle\int _{ { 1 }/{ \pi  } }^{ \pi  }{ \dfrac { 1 }{ x } \cdot \sin { \left( x-\dfrac { 1 }{ x }  \right)  } dx } $$, then $$I$$ is equal to

$$\int { \left( \cfrac { 4{ e }^{ x }-25 }{ 2{ e }^{ x }-5 }  \right)  } dx=Ax+B\log { \left| 2{ e }^{ x }-5 \right|  } +c$$, then

If $$\displaystyle \int { \cfrac { f(x) }{ \log { (\sin { x } ) }  }  } dx=\log { \left[ \log { \sin { x }  }  \right]  } +c$$, then $$f(x)=$$........

If $$I_n = \int_0^{\pi/4} tan^n \theta d \theta$$, where n is a positive integer, then $$n(I_{n-1} + I_{n +1})$$ is equal to

The solution of the equation $$\dfrac { dy }{ dx } =\dfrac { x\left( 2\log { x } +1 \right)  }{ \sin { y } +y\cos { y }  } $$ is

The value of $$\displaystyle \int_{1/n}^{(an - 1)/n} \dfrac {\sqrt {x}}{\sqrt {a - x} + \sqrt {x}} dx$$ is equal to

The value of $$\displaystyle\int _{ 0 }^{ \pi  }{ \dfrac { dx }{ 5+3\cos { x }  }  } $$ is