Integrals Test ...

$$\int \dfrac {2x + 5}{\sqrt {7 - 6x - x^{2}}} dx = A\sqrt {7 - 6x - x^{2}} + B\sin^{-1} \left (\dfrac {x + 3}{4}\right ) + C$$
(where $$C$$ is a constant of integration), then the ordered pair $$(A, B)$$ is equal to

$$\displaystyle\int\displaystyle\frac{e^{\cot^{-1}x}}{1+x^2}(x^2-x+1)dx$$ 

$$\displaystyle\int \displaystyle\frac{\cos \alpha}{\sin x\cos (x-\alpha)}dx=$$___________ $$+$$c where $$0 < x < \alpha < \pi_{/2}$$ and $$\alpha$$-constant.

Let $$I=\displaystyle \int _{ \pi /4 }^{ \pi /3 }{ \cfrac { \sin { x }  }{ x }  } dx$$. Then?

$$\int _{ 0 }^{ 1 }{ x{ \left[ 1-x \right]  }^{ 11 } } dx=........$$

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

What is $$\displaystyle \int_{0}^{2\pi}\sqrt {1 + \sin \dfrac {x}{2}}dx$$ equal to?

$$\int _{ 0 }^{ 5 }{ \sqrt { 25-{ x }^{ 2 } }  } dx=.........$$

The value of $$\displaystyle \int_{0}^{\dfrac {\pi}{4}} (\sqrt {\tan x} +  \sqrt {\cot x})\,\, dx$$ is equal to

$$\int _{ a }^{ b }{ \cfrac { \log { x }  }{ x }  } dx=.......\quad $$ (where $$a,b\in { R }^{ + }$$)