What is the integral of e^{-z}sec^2(x) ?

The integral of e^{-z}sec^2(x) is e^{-z}tan(x)+C

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integral of e^{-z}sec^2(x)

\int e^{- z} sec^{2} (x) d x

e^{- z} tan (x) + C

Solution steps

\int e^{- z} sec^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{- z} \cdot \int sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= e^{- z} tan (x)

Add a constant to the solution

= e^{- z} tan (x) + C

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What is the integral of e^{-z}sec^2(x) ?
The integral of e^{-z}sec^2(x) is e^{-z}tan(x)+C