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

Write the integral as a limit as approaches .
Apply basic rules of exponents.
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.
Evaluate the limit.
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 .
Evaluate.
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