Calculus Examples

Find the Antiderivative f(x)=sin(2x)
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
Let . Then , so . Rewrite using and .
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Step 3.1
Let . Find .
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Step 3.1.1
Differentiate .
Step 3.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.1.3
Differentiate using the Power Rule which states that is where .
Step 3.1.4
Multiply by .
Step 3.2
Rewrite the problem using and .
Step 4
Combine and .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
The integral of with respect to is .
Step 7
Simplify.
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Step 7.1
Simplify.
Step 7.2
Combine and .
Step 8
Replace all occurrences of with .
Step 9
Reorder terms.
Step 10
The answer is the antiderivative of the function .