How do I know when to integrate using by parts or by substitution?

When integrating a function which can be defined as a combination of two functions, it can be difficult to tell whether or not to use by parts. We can spot when to use by parts if we look at the composite function, split it into an f(x) and g(x) and check if the functions has different forms of x, i.e normal polynomial, trigonometric and logarithmic.For example: Determine \xsin(x)dx (\ = integral)Let f(x) = x, g(x) = sin(x) These functions are of different forms so we apply the by parts formula (uv - \v'u) where f(x) = u and g'(x) = v-xcos(x) - -cos(x)dx = -xcos(x) + sin(x) + c

EK
Answered by Eesa K. Maths tutor

3054 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the gradient of the curve with the equation y = x^3+7x^2+1 at x=2


Find the first three terms of the binomial expansion of (3 + 6x)^(1/2).


Given that y=π/6 at x=0 solve the differential equation,dy/dx=(e^x)cosec2ycosecy


How can I recognise when to use a particular method for finding an integral?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning