Calculus Examples

Find the Antiderivative f(x) = square root of x(6+5x)
Step 1
The function can be found by finding the indefinite integral of the derivative .
Step 2
Set up the integral to solve.
Step 3
Integrate by parts using the formula , where and .
Step 4
Simplify.
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Step 4.1
Combine and .
Step 4.2
Combine and .
Step 4.3
Combine and .
Step 4.4
Multiply by .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
By the Power Rule, the integral of with respect to is .
Step 7
Simplify the answer.
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Step 7.1
Rewrite as .
Step 7.2
Simplify.
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Step 7.2.1
Combine and .
Step 7.2.2
Multiply by .
Step 7.2.3
Multiply by .
Step 7.2.4
Multiply by .
Step 7.2.5
Factor out of .
Step 7.2.6
Cancel the common factors.
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Step 7.2.6.1
Factor out of .
Step 7.2.6.2
Cancel the common factor.
Step 7.2.6.3
Rewrite the expression.
Step 7.2.7
Combine the numerators over the common denominator.
Step 7.2.8
Subtract from .
Step 7.2.9
Factor out of .
Step 7.2.10
Cancel the common factors.
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Step 7.2.10.1
Factor out of .
Step 7.2.10.2
Cancel the common factor.
Step 7.2.10.3
Rewrite the expression.
Step 7.2.10.4
Divide by .
Step 8
The answer is the antiderivative of the function .