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

Let . Find .

Rewrite.

Divide by .

Substitute the lower limit in for in .

Simplify.

Multiply by .

Add and .

Substitute the upper limit in for in .

Simplify.

Multiply by .

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.

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 .

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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