$\int {\left( {{x^{{3 \over 4}}} + {x^{-{1 \over 2}}} - 5} \right)} dx$

$\int {\sqrt x \left( {\sqrt x  - 2x} \right)} \left( {x + 1} \right)dx$

$\int {\left( {{x^{ - 3}} - 2{x^{ - 2}} + 4x + 1} \right)} dx$

$\int {\left[ {\left( {2x + 3{x^{ - 2}}} \right)\left( {{x^2} - {1 \over x}} \right) + 3{x^{ - 3}}} \right]} dx$