Calculus Examples

Evaluate the Integral integral of tan(2x)^2 with respect to x
Step 1
Let . Then , so . Rewrite using and .
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Step 1.1
Let . Find .
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Step 1.1.1
Differentiate .
Step 1.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3
Differentiate using the Power Rule which states that is where .
Step 1.1.4
Multiply by .
Step 1.2
Rewrite the problem using and .
Step 2
Combine and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Using the Pythagorean Identity, rewrite as .
Step 5
Split the single integral into multiple integrals.
Step 6
Apply the constant rule.
Step 7
Since the derivative of is , the integral of is .
Step 8
Simplify.
Step 9
Replace all occurrences of with .
Step 10
Simplify.
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Step 10.1
Multiply by .
Step 10.2
Apply the distributive property.
Step 10.3
Cancel the common factor of .
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Step 10.3.1
Factor out of .
Step 10.3.2
Cancel the common factor.
Step 10.3.3
Rewrite the expression.
Step 10.4
Combine and .
Step 11
Reorder terms.