intrgral of t^2 cos (1-t^3) dt

Question

Evaluate:

S= Integrate sign

 

S  t^2 cos (1-t ^3) dt

Answer 1

∫t²(cos(1-t³)dt.

Let x=1-t³, then dx=-3t²dt, so t²dt=-dx/3 and cos(1-t³)=cos(x).

∫t²(cos(1-t³)dt=-⅓∫cos(x)dx=-⅓sin(x)+C, where C is an integration constant.

Replacing x: C-⅓sin(1-t³) is the indefinite integral.