How do I integrate x^2 * sin(x) using integration by parts?
I am stuck on the integration of x squared times sin x. I tried applying integration by parts once but I end up with another integral that still needs parts. How many times do I need to apply it and is there a pattern to follow?
1 Answer
SGSneha Gupta
✓ Accepted
· 13d ago
▲ 10
Apply integration by parts twice. First let u = x^2 and dv = sin(x)dx, giving du = 2x dx and v = -cos(x). After first application you get -x^2 cos(x) + integral of 2x cos(x) dx. Apply parts again to that remaining integral with u = 2x and dv = cos(x)dx. Final answer: -x^2 cos(x) + 2x sin(x) + 2cos(x) + C.
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