Evaluate integral of x/((1+x^2)^(1/2)) with respect to x

Factor .
Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Add and .
Rewrite the problem using and .
Simplify.
Multiply and .
Move to the left of .
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, .
Combine and .
Move the negative in front of the fraction.
By the Power Rule, the integral of with respect to is .
Simplify.
Simplify.
Simplify.
Combine and .
Combine and .
Cancel the common factor.
Divide by .
Replace all occurrences of with .
Evaluate integral of x/((1+x^2)^(1/2)) with respect to x

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