Calculus Examples

Find the Antiderivative 2x(1+3x^3)
Step 1
Write as a function.
Step 2
The function can be found by finding the indefinite integral of the derivative .
Step 3
Set up the integral to solve.
Step 4
Multiply .
Step 5
Simplify.
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 5.3
Multiply by by adding the exponents.
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Step 5.3.1
Move .
Step 5.3.2
Multiply by .
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Step 5.3.2.1
Raise to the power of .
Step 5.3.2.2
Use the power rule to combine exponents.
Step 5.3.3
Add and .
Step 6
Split the single integral into multiple integrals.
Step 7
Since is constant with respect to , move out of the integral.
Step 8
By the Power Rule, the integral of with respect to is .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
By the Power Rule, the integral of with respect to is .
Step 11
Simplify.
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Step 11.1
Simplify.
Step 11.2
Simplify.
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Step 11.2.1
Combine and .
Step 11.2.2
Cancel the common factor of .
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Step 11.2.2.1
Cancel the common factor.
Step 11.2.2.2
Rewrite the expression.
Step 11.2.3
Multiply by .
Step 11.2.4
Combine and .
Step 12
The answer is the antiderivative of the function .