AP Calculus BC / Unit 6: Integration and Accumulation of Change
6.11 Integrating Using Integration by Parts
Notes
$$\int u\,dv=uv-\int v\,du$$
- Choose $u$ as the part that gets simpler when differentiated (often by LIATE: logs, inverse trig, algebraic, trig, exponential).
Practice
$\displaystyle \int xe^x\,dx=$
$u=x$, $dv=e^xdx$.
For $\displaystyle \int x\cos x\,dx$, the best choice of $u$ is:
Differentiating $x$ gives 1.
$\displaystyle \int\ln x\,dx=$
$u=\ln x$, $dv=dx$.
Ready for more? Take the Unit 6 test.