Calculus Examples

Evaluate the Integral integral of (sin(x))/(1-cos(x)) 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.
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Step 1.1.2.1
By the Sum Rule, the derivative of with respect to is .
Step 1.1.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 1.1.3
Evaluate .
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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
The derivative of with respect to is .
Step 1.1.3.3
Multiply by .
Step 1.1.3.4
Multiply by .
Step 1.1.4
Add and .
Step 1.2
Rewrite the problem using and .
Step 2
The integral of with respect to is .
Step 3
Replace all occurrences of with .