Evaluate the integral: \(\int { x^2\ +\ 4x\over x^3\ +\ 6x^2\ +\ 5 } dx\)

Evaluate the integral: \(\int {dx\over x^2\ +\ 16}\)

If \(\int {(ax\ +\ b)^2dx\ =\ f\ (x)\ +\ c}\), find f (x).

\(\int tan^{-1}(cot\ x)dx.\)

\(\int \sqrt{tan\ x}(1+tan^2\ x)\ dx.\)

\(\int { { cos }^{ 3 } } xdx\)

\(\int { { sin }^{ 2 }x{ \ cos }^{ 2 }x } dx\)

\(\int { { e }^{ x } } \left[ cotx+logsinx \right] dx\)

Evaluate : \(\int _{ a }^{ b }{ \frac { logx }{ x } } dx\)

Evaluate : \(\int _{ e }^{ { e }^{ 2 } }{ \frac { dx }{ xlogx } } \)

Find the following integrals:
\((i)\int { \frac { { x }^{ 3 }-1 }{ { x }^{ 2 } } } dx\)
\((ii) \int\left(x^{\frac{2}{3}}+1\right) d x\)
\((iii) \int\left(x^{\frac{3}{2}}+2 e^x-\frac{1}{x}\right) d x\)

Find the following integrals: 
\((i) \int { (\sin { x } } +\cos { x } )dx\)
\((ii) \int { co\sec { x } ( } co\sec { x } +\cot { x } )dx\)
\((iii) \int { \frac { 1-\sin { x } }{ \cos ^{ 2 }{ x } } } dx\)

Find: \(\int _{ 0 }^{ 2 }{ { e }^{ x } } dx\) as the limit of a sum.

Find:\(\int { \frac { \sin { 2x } \cos { 2x }\space dx}{ \sqrt { 9-\cos ^{ 4 }{ (2x) } } } }\)

Find the integral: \(\int \frac{x^3+3 x+4}{\sqrt{x}} d x\)

Evaluate the integral: \(\int {e^x\over\sqrt{5-4e^x-e^{2x}}}dx\)

Evaluate the integral: \(\int{sin\ x\over sin\ x + cos\ x}dx\)

Evaluate the integral: \(\int log (1+x^2)dx.\)

\(\int { { e }^{ x }\left( \frac { \sin { 4x-4 } }{ 1-\cos { 4x } } \right) } dx\)

Find : \(\int { \frac { { x }^{ 2 }+x+1 }{ ({ x }^{ 2 }+1)(x+2) } } dx.\)