# 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

Evaluate integral from 1 to 7 of ( natural log of (x)^2)/(x^3) with respect to x
Rewrite as .
Since is constant with respect to , move out of the integral.
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 .
Integrate by parts using the formula , where and .
Simplify.
Combine and .
Multiply and .
Raise to the power of .
Use the power rule to combine exponents.
Since is constant with respect to , move out of the integral.
Simplify.
Multiply by .
Multiply by .
Since is constant with respect to , move out of the integral.
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 .
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 .
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.
Evaluate.
Simplify each term.
Rewrite as .
Simplify by moving inside the logarithm.
One to any power is one.
The natural logarithm of is .