How do I know which method of integration to use?

First of all, it is very important to simply learn some common integrations by rote (e.g trig functions, exponentials, polynomials, 1/x). If you know these well, it will often be easy to spot which technique to use when integrating a seemingly difficult function.

If you are in a situation where you have to integrate a function comprised of two different types of function, such as f(x)=xe^x, integration by parts can be useful (i.e substitute u for one part of the function and v' for the other, such that the you now have to integrate uv' with solution uv - integral(vu'dx)). It is often a good idea when choosing what to use as and v to choose as u whatever simplifies the most when you differentiate. For example, in the above function I would make u=x and v'=e^x so that u'=1 and v=e^x. Then the integral of vu' is simply the integral of e^x which is quite simple.

Unless you are given case like this, integration by inspection (just by looking at it and using your known results) is always possible but can sometimes be hard to spot. If this is the case, it can be useful to use a clever substitution to help you. (Have a look at my solution to the integral of f(x)=x(1-x)^6 for an example of this

Olaoluwa O. GCSE Further Mathematics  tutor, A Level Further Mathemat...

10 months ago

Answered by Olaoluwa, an A Level Maths tutor with MyTutor

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


£20 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics + 1 more

Further Mathematics

“About me: Hi I'm Ayyub, current student at Bristol university studying Maths with a masters. I'd like to think of myself as a very patient person when it comes to working with others and a generally friendly and approachable person, q...”

MyTutor guarantee

£20 /hr

Charley H.

Degree: Mathematics and Economics (Bachelors) - Liverpool University

Subjects offered: Maths, Economics


“About Myself: I am currently studying Mathematics and Economics at The University of Liverpool. I have always enjoyed these two subjects, especially maths, and I hope I can help in assisting you achieve your goal- whether that be pass...”

MyTutor guarantee

£20 /hr

Larry R.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“I am a Mathematics student at Warwick University. My enthusiasm for all things mathematical has no bounds and it's not just Maths that interests me but also the way that people learn it.  I am patient and friendly. Over the last few y...”

About the author

Olaoluwa O.

Currently unavailable: for new students

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered: Maths, Latin+ 1 more

Further Mathematics

“About me I am a 19 year old Mathematics & Philosophy student at Durham University. I am particularly interested in the analytic side of pure mathematics as well as Latin language, two subjects which I enjoyed studying through to A lev...”

You may also like...

Posts by Olaoluwa

How do I know which method of integration to use?

How do you translate long, complex Latin sentences?

How would you integrate a function like f(x)=x(1-x)^6?

Other A Level Maths questions

How would you sketch the curve of a graph?

x = 2t + 5, y = 3 + 4/t. a) Find dy/dx at (9.5) and b) find y in terms of x.

How do you differentiate (3x+cos(x))(2+4sin(3x))?

At x=3, is the polynomial y= (4/3)x^3 -6x^2 + 11 at a maxima or minima?

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