Evaluate \(\int _{ 0 }^{ 1 }{ \frac { { e }^{ x } }{ 1+{ e }^{ 2x } } dx } \)

Find the area of the region enclosed by the curve y = \(\sqrt x\) + 1, the axis of x and the lines x = 0, x = 4.

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tanx)dx } =0\)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { e }^{ 3x } } cosxdx\)

Evaluate \(\int _{ 0 }^{ \infty }{ \left( { a }^{ -x }-{ b }^{ -x } \right) } dx\)