Integrals Test ...

The value of $$\int_{-1}^{3}[tan^{-1}(\frac{x}{x^{2}+1})+tan^{-1}(\frac{x^{2}+1}{x})]dx$$ 

The value(s) of $$\int _{ 0 }^{ 1 }{ \cfrac { { x }^{ 4 }{ \left( 1-x \right)  }^{ 4 } }{ 1+{ x }^{ 2 } }  } dx$$ is (are)

Evaluate : $$\int { \cfrac { dx }{ x\cos { x }  }  } $$

If $$G(x) = \begin{vmatrix}f(x)f(-x) & 0 & x^{4}\\ 3 & f(x) - f(-x) & \cos x\\ x^{4} & 2x & f(x)f(-x)\end{vmatrix}$$, then $$\int_{-2}^{2} x^{4}G(x)dx$$ is equal to

$$\int _{ 0 }^{ 1 }{ \frac { x }{ 1+\sqrt { x }  } dx= }$$

If the primitive of $$\frac{1}{{f\left( x \right)}}\,$$ is equal to $$\,{\left\{ {f\left( x \right)} \right\}^2} + c$$,then f(x) is

If $$\int \sqrt{\dfrac{x-5}{x-7}}dx=a\sqrt{x^{2}-12x+35+log}|x-6+\sqrt{x^{2}-12x+35}|+C$$ then $$A$$=

Consider $$f ( x ) = \int _ { 0 } ^ { \pi } \frac { \ln ( 1 + x \cos \theta ) } { \cos \theta } d \theta$$
Range of $$f ( x )$$ is

$$\int _ { 0 } ^ { \pi ^ { 2 } / 4 } \sin \sqrt { x } d x$$ is

The value of $$\displaystyle \int _{0}^{\pi/2} \log{\sin{x}}dx$$ is