Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you integrate #int x^3 sin x^2 dx # using integration by parts?

1 Answer

Sep 24, 2016

# 1/2(sin(x^2)-x^2cos(x^2))+C#

Explanation:

#d/dx(x^2cos(x^2))=2xcos(x^2)-2x^3sin(x^2)#

but #2xcos(x^2)= d/dx(sin(x^2))# so

#d/dx(x^2cos(x^2)) = d/dx(sin(x^2))-2x^3sin(x^2)#

then

#int x^3sin(x^2)dx = 1/2(sin(x^2)-x^2cos(x^2))+C#

Related questions

See all questions in Integration by Parts

Impact of this question

4124 views around the world

You can reuse this answer
Creative Commons License