Calculus Examples

Evaluate the Integral integral of 2cos(x)^2 with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Use the half-angle formula to rewrite as .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Simplify.
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Step 4.1
Combine and .
Step 4.2
Cancel the common factor of .
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Step 4.2.1
Cancel the common factor.
Step 4.2.2
Rewrite the expression.
Step 4.3
Multiply by .
Step 5
Split the single integral into multiple integrals.
Step 6
Apply the constant rule.
Step 7
Let . Then , so . Rewrite using and .
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Step 7.1
Let . Find .
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Step 7.1.1
Differentiate .
Step 7.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 7.1.3
Differentiate using the Power Rule which states that is where .
Step 7.1.4
Multiply by .
Step 7.2
Rewrite the problem using and .
Step 8
Combine and .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
The integral of with respect to is .
Step 11
Simplify.
Step 12
Replace all occurrences of with .