Integration by Parts Worksheet with Answer Key

What's on the worksheet

1. Find each integral by parts.
   \displaystyle\int \dfrac{\ln x}{\sqrt{x}}\,dx\displaystyle\int \arctan 3x\,dx
2. Find (6x + 7) 2x\,dx.
3. Evaluate each definite integral exactly, using the definite form of integration by parts.
4. Use tabular integration to find x²(x - 3)^6\,dx.
5. Let I = e^-x 3x\,dx.
6. This problem finds x(x + 1)\,dx for x > -1 in two ways, with u = (x + 1) and dv = x\,dx both times.
7. Arjun's astronomy club counts meteors during a shower.