Integrals Test ...

If $$I_{1}= \displaystyle \int_{x}^{1}\displaystyle \frac{dt}{1+t^{2}}$$ and $$I_{2}= \displaystyle \int_{1}^{1/x}\displaystyle \frac{dt}{1+t^{2}}$$ for $$x> 0$$, then

If $$I_{1}= \displaystyle \int_{0}^{\infty }\displaystyle \frac{dx}{1+x^{4}}$$ and $$I_{2}= \displaystyle \int_{0}^{\infty }\displaystyle \frac{x^{2}}{1+x^{4}}\: dx$$, then

Value of $$\displaystyle \int_{0}^{1}\displaystyle \frac{dx}{\left ( 1+x^{2} \right )\sqrt{1-x^{2}}}$$ is?

The value of $$\displaystyle \int_{1/2}^{1}\displaystyle \frac{dx}{x\sqrt{3x^{2}+2x-1}}$$ is?

If $$\displaystyle \int_{0}^{\infty }\displaystyle \frac{\log \left ( 1+x^{2} \right )}{1+x^{2}}\: dx= \lambda \displaystyle \int_{0}^{1}\displaystyle \frac{\log \left ( 1+x \right )}{1+x^{2}}\: dx$$ then $$\lambda $$ equals

If $$I= \displaystyle \int_{1}^{\infty }\displaystyle \frac{x^{2}-2}{x^{3}\sqrt{x^{2}-1}}\: dx$$, then $$I$$ equals

Value of $$\displaystyle \int_{a}^{\infty }\displaystyle \frac{dx}{x^{4}\sqrt{a^{2}+x^{2}}}$$ is

The value of $$\displaystyle \int _{ 1/2 }^{ 2 }{ \frac { 1 }{ x } \csc ^{ 101 }{ \left( x-\frac { 1 }{ x }  \right)  } dx } $$ is?

Value of $$\displaystyle \int_{0}^{16}\displaystyle \frac{x^{1/4}}{1+x^{1/2}}\: dx$$ is

If $$\displaystyle \frac{\pi }{4}< \alpha < \displaystyle \frac{\pi }{2}$$, value of $$\displaystyle \int_{-\pi /2}^{\pi /2}\displaystyle \frac{\sin 2x}{\sqrt{1+\sin 2\alpha \sin x}}$$ is