Find an approximate value of \(\int _{ 1 }^{ 1.5 }{ xdx } \) by applying the left-end rule with the partition {1.1, 1.2, 1.3, 1.4, 1.5}.

Evaluate :\(\int _{ 0 }^{ \frac { \pi }{ 3 } }{ \frac { sec\ x\ tan\ x }{ 1+{ sec }^{ 2 }x } dx } \)

Evaluate :\(\int _{ 0 }^{ 9 }{ \frac { 1 }{ x+\sqrt { x } } dx } \)

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

Evaluate: \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { cos\theta }{ (1+sin\theta )(2+sin\theta ) } } d\theta \)

Evaluate: \(\int _{ 0 }^{ \frac { 1 }{ \sqrt { 2 } } }{ \frac { { sin }^{ -1 }x }{ { (1-{ x }^{ 2 }) }^{ \frac { 3 }{ 2 } } } dx } \)

If f (x) = f (a + x), then \(\int _{ 0 }^{ 2a }{ f(x)dx=2\int _{ 0 }^{ a }{ f(x)dx } } \)

Evaluate the following definite integrals:
\(\int _{ 0 }^{ 1 }{ \frac { 1-{ x }^{ 2 } }{ { (1+{ x }^{ 2 }) }^{ 2 } } } dx\)

Evaluate the following integrals using properties of integration:
\(\int _{ -5 }^{ 5 }{ xcos } \left( \frac { { e }^{ x }-1 }{ { e }^{ x }+1 } \right) dx\)

Evaluate the following integrals using properties of integration:
\(\int _{ 0 }^{ 2\pi }{ xlog\left( \frac { 3+cos\ x }{ 3-cos\ x } \right) } dx\)