Integration of a composite function

[Nisheeth]

Homework Statement

The question I have is a more general one, but one I can't find an anser to since I don't have any access to a book on integration at the moment.

How do we Integrate a composite function.

∫f(g(x)) dx

Homework Equations

The Attempt at a Solution

 

[micromass]

A technique that might work is substitution. But it depends on the specific values of f and g, really.

 

[Nisheeth]

Ok, so that means that there is not general method like for integration, as there is for differentiation?
Nonetheless thanks!

 

[algebrat]

Ok, so that means that there is not general method like for integration, as there is for differentiation?
Nonetheless thanks!

If you have ∫f(g(x))g'(x)dx, then this is equal to the simpler ∫f(u)du. This is the analogue to the chain rule for integrals. I say it in words as, the derivative of the inside must appear outside.