# Evaluate integral from 1 to e of (x^2-1)/x with respect to x

Split the fraction into multiple fractions.
Split the single integral into multiple integrals.
Simplify.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Raise to the power of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Move the negative in front of the fraction.
By the Power Rule, the integral of with respect to is .
Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Substitute and simplify.
Evaluate at and at .
Evaluate at and at .
Simplify.
Combine and .
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.
Multiply by .
Evaluate.
Use the quotient property of logarithms, .
Combine the numerators over the common denominator.
is approximately which is positive so remove the absolute value
The absolute value is the distance between a number and zero. The distance between and is .
Simplify the numerator.
Divide by .
The natural logarithm of is .
Multiply by .
Subtract from .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate integral from 1 to e of (x^2-1)/x with respect to x