(1) S xe^xdx
(2) S xsinxdx
(3) S lnxdx
(4) S (e^x)cosxdx
INTEGRATION BY PARTS
The formula for integration by parts is:
The hard part is knowing when to use this formula and how to choose appropriate u and dv.
Here are some examples of problems that you can solve using the method of integration by parts, and explanations on how to solve them.
Let u = x and dv = exdx. That means du = 1dx and v = ex.
Plug those values for u, v, du, and dv into the integration by parts formula:
∫xexdx = (x)(ex) - ∫(ex)(dx)
Solve the integral:
∫xexdx = xex - ex + c
Now, what if we had let u = ex and dv = xdx? Then du = exdx and v = ...
This posting has 4 examples of problems solved using the method of integration by parts. These involve integrating functions that include the terms e^x, ln(x), sin(x), and cos(x). The solution includes the formula for integration by parts as well as step-by-step explanations.