(Original post by TimothyTankT)
Basically we have been given a sheet with all the standard integrals we should know.
I don't however understand this one:
Integral f'(g(x))g'(x)dx = f(g(x)) + c
Would someone using latex just give an example using a simple equation as then I should see it much clearer!
It is the rule for the integration of compodite functions and the base of this notation
is the definition of undetermined integral namely so that
If function f in composite, for example f(g(x)), then from the chain rule where f' is derivative of outer function
substituting g(x) in x multiplied by the derivative of inner function, g'(x).
So integrating this
Generally where H is the primitive function of h.
because the primitive function of 1/x is ln|x| and the derivative of cosx is -sinx.