# Evaluate integral of x First, divide ( square root of two x minus one) with respect to x

Evaluate integral of x/( square root of 2x-1) with respect to x
Let . Then , so . Should be rewritten using and .
Let . Find .
Rewrite.
Divide by .
Rewrite the problem using and .
Simplify.
First, multiply by .
Use the distributive law.
The common factor should be canceled of .
Cancel the common factor.
Reformulate the expression.
The common factor should be canceled.
Cancel the common factor.
Rewrite the expression.
Multiply and .
First, multiply by .
Since is constant with respect to , move out of the integral.
Apply basic rules of exponents.
Use to rewrite as .
Move out of the denominator by raising it to the power.
Multiply the exponents in .
Apply the power rule when multiplying the exponents, .
Combine and .
Put the negative in front of the fraction.
Expand .
Apply the distributive property.
Raise to the power of .
Use the power rule to Add exponents.
Write as a fraction with a common denominator.
Add numerators over the common denominator.
Subtract from .
Multiply by .
Split the single integral into multiple integrals.
By the Power Rule, the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Simplify.
Replace all occurrences of with .
Combine and .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Clarify the numerator.
Factor out of .
Move .
Factor out of .
Factor out of .
Factor out of .
Divide by .
Simplify.