Here, we have , which tells us we will need to use the method of integration by parts 4 times. Luckily, there is a quicker way for integrals involving powers of multiplied by a function such as or or . The method is called the tabular method. Make a chart with three columns. The first column will contain alternating +, -, +, ... starting with +. The second column will start out with and each row below will contain the derivative of the function above. Keep going until you reach 0 as a derivative. The third column contains and every subsequent row contains the integral of the function below.
So we have the answer already. When multiplying in the first row, as you can see by the arrows, multiply the by the in the same row and by the in the row below. Do all of these multiplications and add them together to get the answer.