Integration problem

Question

Solve step by step.

Answer 1

The integration expression is .

Consider the function .

Let (x² + 2x - 2) = t² ---> (2x + 2)dx = 2t dt ---> (x + 1)dx = t dt.

.

Consider the function .

Write the quadratic expression in the complete square form.

= x².+ 2x - 2

=(x + 1)²  - 1 - 2

=(x + 1)²  - 3