Evaluate integral of sec(1-x)tan(1-x) with respect to x

Math
Let . Then , so . Rewrite using and .
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Let . Find .
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Differentiate .
Differentiate using the chain rule, which states that is where and .
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To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Since is constant with respect to , the derivative of with respect to is .
Move to the left of .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Rewrite the problem using and .
Since is constant with respect to , move out of the integral.
Replace all occurrences of with .
Evaluate integral of sec(1-x)tan(1-x) with respect to x

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