Integrate by parts using the formula , where and .

Combine and .

Let . Find .

Differentiate .

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

Differentiate using the Power Rule which states that is where .

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

Add and .

Substitute the lower limit in for in .

Simplify.

Raising to any positive power yields .

Add and .

Substitute the upper limit in for in .

Simplify.

One to any power is one.

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.

Multiply and .

Move to the left of .

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

The integral of with respect to is .

Combine and .

Evaluate at and at .

Evaluate at and at .

Simplify.

Multiply by .

Multiply by .

Multiply by .

Add and .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Move to the left of .

Simplify the numerator.

The exact value of is .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Rewrite in a factored form.

Multiply .

Multiply by .

Simplify by moving inside the logarithm.

Raise to the power of .

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate integral from 0 to 1 of arctan(x) with respect to x