Integrals Test ...

$$\displaystyle\int^{\pi /3}_0\frac{\cos \theta}{5-4\sin \theta}d\theta$$ equal to.

Consider $$I=\displaystyle \int^{\pi}_{0}\displaystyle\frac{xdx}{1+\sin x}$$. What is I equal to?

The value of $$\int _{ 1/3 }^{ 3 }{ \cfrac { \tan { \left( { x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } }  \right)  }  }{ \sin { \left( x+\cfrac { 1 }{ x }  \right)  }  }  } \cfrac { dx }{ x } $$ is 

Let $$I_{1} =\displaystyle  \int_{0}^{1}\dfrac {e^{x}dx}{1 + x}$$ and $$I_{2} = \displaystyle \int_{0}^{1} \dfrac {x^{2}dx}{e^{x^{3}}(2 - x^{3})}$$, then $$\dfrac {I_{1}}{I_{2}}$$ is

$$\displaystyle\int^{\pi}_0\sqrt{|\cos x|-|\cos^3x|}dx$$ is?

The value of the definite integral $$\displaystyle\int^{\pi/2}_{0}\left(\cos ^{10}x\cdot \sin 12x\right)dx$$, is equal to.

$$\int { { x }^{ 4 }{ e }^{ 2x } } dx=$$

The value of $$\int^3_{1/3}\dfrac{tan(x^2-\dfrac{1}{x^2})}{sin(x+\dfrac{1}{x}) }\dfrac{dx}{x}$$ is 

$$\displaystyle \int _{ 0 }^{ x }{ \cfrac { \sin { x }  }{ 1+\cos ^{ 2 }{ x }  }  } dx=\pi \cfrac { \cos { \alpha  }  }{ 1-\sin ^{ 2 }{ \alpha  }  } $$

$$\int _{ 0 }^{ \pi /2 }{ \sin ^{ 8 }{ x } \cos ^{ 2 }{ x } dx } $$ is equal to