Question

Evaluate the integral

∫ cos³ 5x dx

Answer 1

∫ cos³ 5x dx

=∫ cos² 5x*cos5x dx

=∫ (1-sin² 5x)*cos5x dx

sin5x=t

dt/dx=5cos5x

dt/5=cos5xdx

=(1/5)∫(1-t²)*dt

=(1/5)(t-t^3/3)+c

=(1/5)(sin(5x)-sin^3(5x))+c