Dear Student, ∫secxdtt92×t=∫secx dtt92+1=secx∫t-112dt= secx×t-112+1-112+1+C= -2secx9×secx+tanx-92+CRegards

Solve this.

Dear Student, \int \frac{secxdt}{t^{\frac{9}{2}} \times t} = \int \frac{secx dt}{t^{\frac{9}{2} + 1}} = secx \int t^{\frac{- 11}{2}} dt = secx \times (\frac{t^{\frac{- 11}{2} + 1}}{\frac{- 11}{2} + 1}) + C = \frac{- 2 secx}{9} \times {(secx + tanx)}^{\frac{- 9}{2}} + C Regards