Evaluate the integration of : (co3x-x^2)(sin3x-x^3)dx?

1 Answer
May 1, 2018

I=1/3ln(abs(sin(3x)-x^3))+C

Explanation:

We want to solve

I=int(cos(3x)-x^2)/(sin(3x)-x^3)dx

Make a substitution

color(blue)(u=sin(3x)-x^3=>du=3(cos(3x)-x^2)dx

I=int(cos(3x)-x^2)/(u*3(cos(3x)-x^2))du

color(white)(I)=1/3int1/udu

color(white)(I)=1/3ln(abs(u))+C

Substitute back color(blue)(u=sin(3x)-x^3)

I=1/3ln(abs(sin(3x)-x^3))+C