7.8: Homework- Integration by Parts
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- Solve each of the following using integration by parts:
- ∫xcos(x)dx
xsin(x)+cos(x)+Cans
- ∫(4x−1)cos(x)dx
(4x−1)sin(x)+4cos(x)+Cans
- ∫xsin(x)dx.
−xcos(x)+sin(x)+Cans
- ∫xexdx.
xex−ex+Cans
- ∫ln(x)dx. (Hint: Let u=ln(x) and v′=1)
xln(x)−xans
- ∫xcos(x)dx
- Watch the following Khan Academy video: Integration by parts twice
- Use integration by parts to solve ∫x2cos(x)dx.
x2sin(x)+2xcos(x)−2sin(x)+Cans
- Use integration by parts to solve ∫x3exdx.
x3ex−3x2ex+6xex−6ex+Cans
- Watch the following Khan Academy video: Integration by parts with e and cos together.
- Use integration by parts to find ∫exsin(x)dx.
sin(x)ex−cos(x)ex2+Cans
- Two part question:
- Use u-substitution to find ∫sin(2x)dx and ∫cos(2x)dx.
−12cos(2x) and 12sin(2x)ans
- Use integration by parts to find ∫xsin(2x)dx.
−12xcos(2x)−14sin(2x)ans
- Use u-substitution to find ∫sin(2x)dx and ∫cos(2x)dx.