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Calculus Examples
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
Use to rewrite as .
Step 4
Move out of the denominator by raising it to the power.
Step 5
Step 5.1
Apply the power rule and multiply exponents, .
Step 5.2
Combine and .
Step 5.3
Move the negative in front of the fraction.
Step 6
Step 6.1
Apply the distributive property.
Step 6.2
Apply the distributive property.
Step 6.3
Raise to the power of .
Step 6.4
Use the power rule to combine exponents.
Step 6.5
Write as a fraction with a common denominator.
Step 6.6
Combine the numerators over the common denominator.
Step 6.7
Subtract from .
Step 6.8
Use the power rule to combine exponents.
Step 6.9
To write as a fraction with a common denominator, multiply by .
Step 6.10
Combine and .
Step 6.11
Combine the numerators over the common denominator.
Step 6.12
Simplify the numerator.
Step 6.12.1
Multiply by .
Step 6.12.2
Subtract from .
Step 7
Split the single integral into multiple integrals.
Step 8
Since is constant with respect to , move out of the integral.
Step 9
By the Power Rule, the integral of with respect to is .
Step 10
By the Power Rule, the integral of with respect to is .
Step 11
By the Power Rule, the integral of with respect to is .
Step 12
Step 12.1
Simplify.
Step 12.2
Reorder terms.
Step 13
The answer is the antiderivative of the function .