# How do you find the integral #int t^2(t^3+4)^(-1/2)dt# using substitution?

##### 2 Answers

#### Explanation:

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.

Let

so,

Putting

or

#### Explanation:

Because **the function outside the bracket is a constant #xx#the derivative of the bracket ,** it suggests that we might be able to do this by 'inspection'.

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!.