Use integration by parts to find the integral of xsinx, with respect to x

The integration by parts rule looks like this:

∫ u * v' dx = u * v - ∫ ( v * u' ) dx

Hence in this example, we want to make our u = x and v' = sinx

So we now need to work out what u' and v are:

u' = 1 which is the easier of the two; to work out v, we should integrate v' = sinx, this will give us v = -cosx

Hence if we now subsititute these into the equations, we will find that:

∫ xsinx dx = -xcosx - ∫ (-cosx) dx

= -xcosx - (-sinx) + C (where C is the constant of integration)

= sinx - xcosx + C

Answered by Toby S. Maths tutor

56693 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).


Use the formula 5p + 2q = t to find the value of q when p = 4 and t = 24. 6


Find the differential of (cos2x)^2


Find the stationary point(s) on the curve 2xsin(x)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences