What is the integral of e^xsec^2(e^x-5) ?

The integral of e^xsec^2(e^x-5) is tan(e^x-5)+C

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integral of e^xsec^2(e^x-5)

\int e^{x} sec^{2} (e^{x} - 5) d x

tan (e^{x} - 5) + C

Solution steps

\int e^{x} sec^{2} (e^{x} - 5) d x

Apply u-substitution

= \int sec^{2} (u) d u

Use the common integral:

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

= tan (u)

Substitute back

u = e^{x} - 5

= tan (e^{x} - 5)

Add a constant to the solution

= tan (e^{x} - 5) + C

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What is the integral of e^xsec^2(e^x-5) ?
The integral of e^xsec^2(e^x-5) is tan(e^x-5)+C