How do I integrate by parts?

  • Google+ icon
  • LinkedIn icon

Lets use and example: y=x*sin(x). If we try to integrate this normally, we find it very hard. The integration by parts method splits up the function we are integrating into manageable bits. The formula we use to work this out is:


were the dU is the differential of U and dV is the differential of V. In our example y=x*sin(x), we let U=x and dV=sin(x). To find dU we differentiate x (dU=1). To find V we integrate dV (V=-cos(x)). Now we just stick everything in the formula:

Integral(xsin(x))= x*(-cos(x))-Integral((-cos(x))*1)=-x*cos(x)+sin(x) +C

where C is an arbitrary constant. This is the answer.

- See more at:

Barnaby W. A Level Maths tutor, A Level Further Mathematics  tutor, G...

About the author

is an online A Level Maths tutor with MyTutor studying at Southampton University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss