Calculus Integration by Parts

Question

Which of these integrals requires the method of integration by parts? (4 points)

Answer Choices:

Answer 1

1) You can use u-substitution, so no.

2) This can be solved using integration by parts. Let u = x and v ' = e^3x. Using the DI method is the simplest way.

D I

+ x e^3x

-1 (e^3x)/3

+ 0 (e^3x)/9

Adding the diagonal multiplications:

Integral = x(e^3x)/3 - (e^3x)/9 + C = (3x-1)e^3x/9 + C

3) You can use trig identities to simplify and solve this one

4) You can use the trig reduction formula to simplify and solve this one. However, the reduction formula is derived from integration by parts, i.e. u=cos(x) v ' = cos(x)