Write the integral as a limit as approaches .

Move out of the denominator by raising it to the power.

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by .

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

Substitute and simplify.

Evaluate at and at .

Simplify.

One to any power is one.

Multiply by .

Combine and using a common denominator.

Move .

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

Combine and .

Combine the numerators over the common denominator.

Combine and .

Move to the denominator using the negative exponent rule .

Multiply by .

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Simplify.

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Move the negative in front of the fraction.

Reorder terms.

Take the limit of each term.

Move the term outside of the limit because it is constant with respect to .

Split the limit using the Sum of Limits Rule on the limit as approaches .

Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .

Evaluate the limit of which is constant as approaches .

Multiply by .

Subtract from .

Multiply .

Multiply by .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Evaluate integral from 1 to infinity of 1/(x^3) with respect to x