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

Let . Find .

Rewrite.

Divide by .

Rewrite the problem using and .

First, multiply by .

Add.

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.

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.

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.

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Multiply by .

The common factor should be canceled.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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