Calculus Examples

Find the Antiderivative f(x)=3/(2x-5)-4
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
Split the single integral into multiple integrals.
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Let . Then , so . Rewrite using and .
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Step 5.1
Let . Find .
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Step 5.1.1
Differentiate .
Step 5.1.2
By the Sum Rule, the derivative of with respect to is .
Step 5.1.3
Evaluate .
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Step 5.1.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 5.1.3.2
Differentiate using the Power Rule which states that is where .
Step 5.1.3.3
Multiply by .
Step 5.1.4
Differentiate using the Constant Rule.
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Step 5.1.4.1
Since is constant with respect to , the derivative of with respect to is .
Step 5.1.4.2
Add and .
Step 5.2
Rewrite the problem using and .
Step 6
Simplify.
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Step 6.1
Multiply by .
Step 6.2
Move to the left of .
Step 7
Since is constant with respect to , move out of the integral.
Step 8
Combine and .
Step 9
The integral of with respect to is .
Step 10
Apply the constant rule.
Step 11
Simplify.
Step 12
Replace all occurrences of with .
Step 13
The answer is the antiderivative of the function .