csc-2019-x-sec-5-x-tan-2-x-dx-

Question Number 60938 by aliesam last updated on 27/May/19

\int \frac{{c s c}^{2019} (x)}{{s e c}^{5} (x)} {t a n}^{2} (x) d x

Commented by Prithwish sen last updated on 27/May/19

\int \frac{\cos^{3} x}{\sin^{2017} x} dx = \int \frac{(1 - \sin^{2} x) cosx}{\sin^{2017} x} dx

put sinx = v

then cosx dx = dv

= \int \frac{(1 - v^{2}) dv}{v^{2017}}

= \int (v^{- 2017} - v^{- 2015}) dv