Expert: Abe Mantell - 5/30/2005

Question
Integral of (2sin(3x)-4cos95x))dx i know you have to probably use U sustitutionon all of them but i dont know how so i need the answeres and the steps so i can know how to do it on a test
Integral of e^x * (1-e^x)dx
Integral of x^3 * cos(x^2)dx
Integral of x^2 * e^3x dx

Answer
Hello Jay,

1. Int(2sin(3x)-4cos(5x)) dx
  = 2cos(3x)/(-3) - 4sin(5x)/5 + C
  = -(2/3)cos(3x)-(4/5)sin(5x)+C

2. Int(e^x(1-e^x)) dx = Int(e^x-e^(2x)) dx
  = e^x - e^(2x)/2 + C
  = e^x - (1/2)e^(2x) + C

3. Int(x^3 cos(x^2)) dx, let u=x^2, then du=2x dx
  = (1/2)Int(2x*x^2 cos(x^2)) dx
  = (1/2)Int(u cos(u)) du
  Now use integration by parts...OK?

4. Use integration by parts.

Abe