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

2895 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the normal to the curve x^3 + 2(x^2)y = y^3 + 15 at the point (2, 1)


If y = 1/(x^2) + 4x, find dy/dx


The point A lies on the curve with equation y = x^(1/2). The tangent to this curve at A is parallel to the line 3y-2x=1. Find an equation of this tangent at A. (PP JUNE 2015 AQA)  


A curve has parametric equations x = 1- cos(t), y = sin(t)sin(2t). Find dy/dx.


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