Integration isn't always simple. Sometimes you just have to replace some of the scary looking stuff with something less scary, and then you can do the integral no problem. By this of course we mean you have to find part of the problem that needs to be replaced by a different variable in order to integrate the simpler part, and then add the hard part back in. The pictures below show a basic form of this method.

Write DOwn the question

Writing down the problem is the first step in solving the problem.

Decide your substitution

Next you need to figure out which part of the equation you have to substitute. Generally, the part you have to substitute U for is going to be he most inside of the equation. In this instance, we have to have a U substitution in place of 2x+3 due to the lack of a product rule with integration.

Derive your substitution

In order to be able to use U as a substitution, the equation must be in terms of U, meaning that you have to derive your substitution equation.

Solve for dx

To be able to substitute du in place of dx, you have to solve for dx. This makes the equation in terms of du, thus allowing the U substitution.

SUBSTITUTE u in your original equation

Now that you have established what your U is and have the integral in terms of U, replace 2x+3 with U to allow you to integrate the variable as if it were a simple X.

Do the Integral

Use (1/n+1)(x^n+1)+C to integrate u^2. If you're not dumb, you should get u^3/3. Don't forget about the 1/2 that came with du, and don't forget your C.

Simplify and replace u

Replace U as (2x+3) and multiply by 1/2. You should have (2x+3)^3/6 +C. Congratulations, you have now completed a U substitution and are now more valuable as a person for knowing how to do so.