How do I integrate by parts?

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...

2 years ago

Answered by Barnaby, an A Level Maths tutor with MyTutor

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


£20 /hr

Kyle R.

Degree: Mathematics (Masters) - Oxford, Corpus Christi College University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics

“Hi! I'm Kyle, a 2nd year Oxford undergraduate studying Maths at Corpus Christi College. I aim to be an understanding and friendly face, whilst being thorough with the material I cover. I've acheived A* grades in Maths, Further Maths a...”

£20 /hr

Noam T.

Degree: Mathematics with Mathematical Physics (Bachelors) - University College London University

Subjects offered: Maths, Physics


“About Myself: I am an undergraduate student at UCL studying Mathematics with Mathematical Physics. Hoping to go into research after my degree, I have a true passion for my subjects and my aim is to pass on that passion to students in ...”

£20 /hr

Jake A.

Degree: Engineering (Masters) - Warwick University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“Who am I? Hey! I’m a personal tutor, general maths enthusiast and am presently studying Engineering at Warwick University. I currently tutor students for Maths / Physics A-level along with Maths, Physics and Chemistry GCSE. I have a g...”

MyTutor guarantee

About the author

£24 /hr

Barnaby W.

Degree: Mathematics (Masters) - Southampton University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“ I have always enjoyed tutoring. I find that it gives me real satisfaction to see a child or student you have helped feel much more confident”

You may also like...

Other A Level Maths questions

How do I simplify surds?

How to sum an arithmetic progression?

How do I multiply 2 matrices?

Below is a question from the Edexcel Maths Core 1 textbook, Solve the equation x^2 + 8x + 10 = 0 using completing the square.

View A Level Maths tutors


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