Q88. If $f ( t ) = \int _ { 0 } ^ { \pi } \frac { 2 x \mathrm {~d} x } { 1 - \cos ^ { 2 } \mathrm { t } \sin ^ { 2 } x } , 0 < \mathrm { t } < \pi$, then the value of $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { \pi ^ { 2 } \mathrm { dt } } { f ( \mathrm { t } ) }$ equals $\_\_\_\_$

Calculate the following indefinite integral: $$\int \frac{x^{2} + x + 2}{x^{3} - px^{2}} \, dx$$ where $p$ is a real constant.

$\int _ { 4 } ^ { 5 } \frac { x + 1 } { x ^ { 2 } - 5 x + 6 } d x$\ What is the value of the integral?\ A) $5 \ln 3 - \ln 2$\ B) $5 \ln 2 - 2 \ln 3$\ C) $3 \ln 2 + 2 \ln 3$\ D) $2 \ln 2 + 3 \ln 3$\ E) $7 \ln 2 - 3 \ln 3$