# Evaluate integral from 0 to 1 of cube root of 1+7x with respect to x

Evaluate integral from 0 to 1 of cube root of 1+7x with respect to x
Let . Then , so . Rewrite using and .
Let . Find .
Rewrite.
Divide by .
Substitute the lower limit in for in .
Simplify.
Multiply by .
Substitute the upper limit in for in .
Simplify.
Multiply by .
The values found for and will be used to evaluate the definite integral.
Rewrite the problem using , , and the new limits of integration.
Combine and .
Since is constant with respect to , move out of the integral.
Use to rewrite as .
By the Power Rule, the integral of with respect to is .
Substitute and simplify.
Evaluate at and at .
Simplify.
Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Raise to the power of .
Combine and .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
One to any power is one.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Multiply and .
Multiply by .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
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