Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Write the fraction using partial fraction decomposition.

Simplify.

Split the single integral into multiple integrals.

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

Let . Find .

Differentiate .

By the Sum Rule, the derivative of with respect to is .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Add and .

Substitute the lower limit in for in .

Add and .

Substitute the upper limit in for in .

Add and .

The values found for and will be used to evaluate the definite integral.

Rewrite the problem using , , and the new limits of integration.

The integral of with respect to is .

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

Let . Find .

Rewrite.

Divide by .

Substitute the lower limit in for in .

Subtract from .

Substitute the upper limit in for in .

Simplify.

Multiply by .

Subtract from .

The values found for and will be used to evaluate the definite integral.

Rewrite the problem using , , and the new limits of integration.

Move the negative in front of the fraction.

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

Combine and .

Move the negative in front of the fraction.

The integral of with respect to is .

Evaluate at and at .

Evaluate at and at .

Remove parentheses.

Simplify each term.

Use the quotient property of logarithms, .

The absolute value is the distance between a number and zero. The distance between and is .

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

Simplify by moving inside the logarithm.

Use the quotient property of logarithms, .

The absolute value is the distance between a number and zero. The distance between and is .

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

The natural logarithm of is .

Multiply .

Multiply by .

Multiply by .

Add and .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate integral from 0 to 2 of 1/(1-x^2) with respect to x