Calculus Examples

Evaluate the Integral integral of sec(4x)tan(4x) 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
Differentiate using the chain rule, which states that is where and .
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Step 1.1.2.1
To apply the Chain Rule, set as .
Step 1.1.2.2
The derivative of with respect to is .
Step 1.1.2.3
Replace all occurrences of with .
Step 1.1.3
Differentiate.
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Step 1.1.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3.2
Differentiate using the Power Rule which states that is where .
Step 1.1.3.3
Simplify the expression.
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Step 1.1.3.3.1
Multiply by .
Step 1.1.3.3.2
Move to the left of .
Step 1.2
Rewrite the problem using and .
Step 2
Apply the constant rule.
Step 3
Replace all occurrences of with .