Integrals Test ...

Evaluate: $$\displaystyle \int_{1/3}^{1}\frac{(x-x^{3})^{1/3}}{x^{4}}dx$$.

$$I=\displaystyle \int _{ 0 }^{ \frac { 1 }{ \sqrt { 2 }  }  }{ \cfrac { { sin }^{ -1 }x }{ { \left( 1-{ x }^{ 2 } \right)  }^{ \frac { 3 }{ 2 }  } } dx }  $$

$$\displaystyle \int_{\log 2}^{t}\frac{d_{X}}{\sqrt{e^{x}-1}}=\frac{\pi}{6}$$, then $$\mathrm{t}=$$

lf $$0<\mathrm{a}<\mathrm{c},\ 0<\mathrm{b}<\mathrm{c}$$ then $$\displaystyle \int_{0}^{\infty}\frac{a^{x}-b^{x}}{c^{x}}dx=$$

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

The solution of the equation $$\displaystyle \int_{\sqrt{2}}^{\mathrm{x}}\frac{\mathrm{d}\mathrm{x}}{\mathrm{x}\sqrt{\mathrm{x}^{2}-1}}=\frac{\pi}{12}$$ is

$$\displaystyle \int_{0}^{\pi/2}\frac{1}{1+4\sin^{2}x}dx=$$