# Find the Antiderivative x(3x-2) Write as a function.
The function can be found by finding the indefinite integral of the derivative .
Set up the integral to solve.
Simplify by multiplying through.
Apply the distributive property.
Simplify the expression.
Reorder and .
Reorder and .
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Simplify.
Simplify.
Simplify.
Combine and .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Combine and .
Combine and .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
The answer is the antiderivative of the function .
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