Exercise
$\int_a^b\left(\tan\left(x\right)^2\sec\left(x\right)^3\right)dx$
Step-by-step Solution
Final answer to the exercise
$-\frac{3}{8}\ln\left|\sec\left(a\right)+\tan\left(a\right)\right|+\frac{5}{8}\tan\left(a\right)\sec\left(a\right)-\frac{1}{4}\sec\left(a\right)^3\tan\left(a\right)+\frac{3}{8}\ln\left|\sec\left(b\right)+\tan\left(b\right)\right|-\frac{5}{8}\tan\left(b\right)\sec\left(b\right)+\frac{1}{4}\sec\left(b\right)^3\tan\left(b\right)+\frac{1}{2}\ln\left|\sec\left(a\right)+\tan\left(a\right)\right|+\frac{-\tan\left(a\right)\sec\left(a\right)}{2}-\frac{1}{2}\ln\left|\sec\left(b\right)+\tan\left(b\right)\right|+\frac{\tan\left(b\right)\sec\left(b\right)}{2}$