Question

Complete the square and find the integral.

Answer 1

Step 1:

The integral is

Rewrite the integral as   

 

Consider .

Differentiate on each side.

Substitute and  in the integral.

Step 2:

Consider 

Assume .

Differentiate on each side.

Substitute and in the integral.

Substitute in above expression.

Step 3:

Consider  .

Integral formula:

 

.

 

Substitute the two integral results in equation (1).

Substitute back .

Solution:

.