Integrals Test ...

$$\displaystyle \int \dfrac{\{f(x) \cdot \phi' (x) - f'(x) \cdot \phi(x) \}}{f(x) \cdot \phi(x)} \{log \,\phi(x) - log \,f(x) \}dx$$ is equal to

$$\int \log _ { 10 } x d x =$$

Evaluate: $$\displaystyle\int \frac { 1 } { ( x + 2 ) \sqrt { x + 1 } } d x $$

Evaluate: $$\int _{ 1/3 }^{ 1 }{ \cfrac { { \left( x-{ x }^{ 3 } \right)  }^{ 1/3 } }{ { x }^{ 4 } }  } dx=$$

Evaluate: $$\displaystyle \int _ { 0 } ^ { \pi / 4 } \sec ^ { 7 } {\theta} \sin ^ { 3 } {\theta} {d \theta} =$$

The value of the defined integral $$\displaystyle \int^{\pi/2}_{0}(\sin x+\cos x)\sqrt {\dfrac {e^{x}}{\sin x}}dx$$ equals

$$\displaystyle \int \frac { 1 - x ^ { 2 } } { \left( 1 + x ^ { 2 } \right) \sqrt { 1 + x ^ { 4 } } } d x$$ is equal to 

$$\displaystyle \int \dfrac { d x } { \sin ^ { 2 } x \cos ^ { 2 } x }$$ equals-

$$\int { { e }^{ x^{ 3 } }+{ x }^{ 2-1 }(3{ x }^{ 4 }+{ 2x }^{ 3 }+{ 2x }^{ 2 }\quad x=h(x)+c } $$ then the value of $$h(1)h(-1)$$.