How do you find the integral #int t^2(t^3+4)^(-1/2)dt# using substitution?
The key to solving any integral is to see what "type" of integral it could classify as. When I see an integral I try to ask myself if it is a substitution, integration by parts, trigonometric, trig sub, or partial fractions integral. In order to know whether or not to use the substitution method is whether or not the integral has both a function and its derivative present in the integral.
For this integral:
Let's do just that.
Because the function outside the bracket is a constant
using the power rule for integration let us 'guess' that teh integral is of teh form
differentiate this using the chain rule:
comparing this with the original question we see that the only difference is the constant
If one can spot integrals by inspection it can save a lot of work!.