Evaluate \(\int { \frac { 3x+2 }{ { \left( x-2 \right) }^{ 2 }\left( x-3 \right) } dx } \)

Evaluate \(\int { \frac { { 3x }^{ 2 }+6x+1 }{ \left( x+3 \right) \left( { x }^{ 2 }+1 \right) } } dx\)

Integrate the following with respect to x.
\(\frac { { 4x }^{ 2 }+2x+6 }{ { \left( x+1 \right) }^{ 2 }\left( x-3 \right) } \)

Integrate the following with respect to x. 
\(\frac { { 3x }^{ 2 }-2x+5 }{ { \left( x-1 \right) }\left( x^{ 2 }+5 \right) } \)

Evaluate \(\int { { \left( \log x \right) }^{ 2 } } dx\)

Evaluate ഽ\(\frac { { xe }^{ x } }{ { \left( 1+x \right) }^{ 2 } } dx\)

Evaluate \(\int\left[\frac{1}{\log x}-\frac{1}{(\log x)^{2}}\right] d x\)

Integrate the following with respect to x.
\(\frac { x }{ 2{ x }^{ 4 }-3{ x }^{ 2 }-2 } \)

Integrate the following with respect to x.
e^x (1+ x) log(xe^x)

Integrate the following with respect to x.
\(\frac { 1 }{ x({ x }^{ 2 }+1) } \)

Integrate the following with respect to x.
\(e^{x}\left[\frac{x-1}{(x+1)^{3}}\right]\)

Evaluate \(\int _{ 2 }^{ 3 }{ \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } } dx\)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { \sin x }{ \sin x+\cos x } } \) dx

Evaluate \(\int _{ 2 }^{ 5 }{ \frac { \sqrt { x } }{ \sqrt { x } +\sqrt { 7-x } } } \) dx

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { { \sin }^{ 7 }x }{ { \sin }^{ 7 }x+{ \cos }^{ 7 }x } dx } \) 

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ \log\left( \frac { 1 }{ x } -1 \right) dx } \)

Evaluate the following using properties of definite integrals:
\(\int _{ 0 }^{ 1 }{ \frac { x }{ ({ 1-x) }^{ \frac { 3 }{ 4 } } } dx } \)

Evaluate the integral as the limit of a sum: \(\int _{ 0 }^{ 1 }{ x } dx\)

Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ (2x+1) } dx\)

Evaluate the integral as the limit of a sum: \(\int _{ 1 }^{ 2 }{ { x }^{ 2 } } \) dx

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ (x+4) } \)dx

Evaluate the following integrals as the limit of the sum:
\(\int _{ 1 }^{ 3 }{ xdx } \)

Evaluate the following integrals as the limit of the sum:
\(\int _{ 1 }^{ 3 }{ (2x+3) } dx\)

Evaluate the following integrals as the limit of the sum:
\(\int _{ 0 }^{ 1 }{ { x }^{ 2 } } dx\)

Evaluate the following integrals:
\(\int _{ 0 }^{ 3 }{ \frac { xdx }{ \sqrt { x+1 } +\sqrt { 5x+1 } } } \)