Let . Find .

Rewrite.

Divide by .

Rewrite the problem using and .

Combine and .

Since is constant with respect to , move out of the integral.

Use to rewrite as .

By the Power Rule, the integral of with respect to is .

Simplify.

Simplify.

Combine and .

Multiply and .

Multiply by .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Replace all occurrences of with .

Reorder terms.

Evaluate integral of square root of 2x+1 with respect to x