# Evaluate integral from one to seven of ( natural log of (x) to the power of two) divide(x to the power of three) with respect to x

Rewrite as .

Since is constant with respect to , move out of the integral.

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

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Multiply by .

Integrate by parts using the formula , where and .

Combine and .

Multiply and .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Since is constant with respect to , move out of the integral.

Multiply by .

Multiply by .

Since is constant with respect to , move out of the integral.

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 .

Simplify.

Combine and .

Combine and .

Move to the denominator using the negative exponent rule .

Substitute and simplify.

Evaluate at and at .

Evaluate at and at .

Simplify.

Raise to the power of .

Multiply by .

One to any power is one.

Multiply by .

Raise to the power of .

Multiply by .

One to any power is one.

Multiply by .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as a product.

Multiply 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.

Simplify each term.

Rewrite as .

Simplify by moving inside the logarithm.

One to any power is one.

The natural logarithm of is .

Add and .

Apply the distributive property.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply .

Combine and .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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