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

Math
Write the integral as a limit as approaches .
Apply basic rules of exponents.
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Move out of the denominator by raising it to the power.
Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Multiply by .
By the Power Rule, the integral of with respect to is .
Simplify the answer.
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Substitute and simplify.
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Evaluate at and at .
Simplify.
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One to any power is one.
Multiply by .
Combine and using a common denominator.
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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 .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Simplify.
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Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Move the negative in front of the fraction.
Reorder terms.
Evaluate the limit.
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Take the limit of each term.
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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.
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Multiply by .
Subtract from .
Multiply .
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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

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