Integrals Test ...

$$\int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { 2x }  }{ { \left( \sin { x } +\cos { x }  \right)  }^{ 2 } }  } dx=......$$

$$\displaystyle \int _0^4\dfrac{2x+3}{x^2+3x+2}dx$$

$$ \int { P\left( x \right) { e }^{ kx }dx=Q\left( x \right) { e }^{ 4x }+C }$$, where $$P(x)$$ is polynomial of degree $$n$$ and $$Q(x)$$ is polynomial of degree $$7$$. Then the value of $$ n+7+k+\lim _{ x\rightarrow \infty  }{ \dfrac { P\left( x \right)  }{ Q\left( x \right)  }  }$$ is:

$$\int { \cos { \left( \log { x }  \right)  }  } dx=............\quad +\quad c$$

$$\displaystyle\int^{\pi}_0\sqrt{2}(1+\cos x)^{7/2}dx=?$$

The value of the integral $$\displaystyle\int^1_0\dfrac{dx}{x^2+2x\cos \alpha +1}$$, where $$0 < \alpha < \dfrac{\pi}{2}$$, is equal to

The value of $$\int \dfrac {1}{\sqrt {\sin^{3}x \cos^{5}x}} dx$$ is

$$\displaystyle \int \dfrac{x \,\ell nx}{(x^2 - 1)^{3/2}}dx$$ equals

$$\displaystyle \int_{1/e}^{e}{|\ln x|dx}$$ equals

$$\int _{ 0 }^{ \pi /4 }{ x.\sec ^{ 2 }{ x } dx=? }$$