What is the integral of ((e^x))/(cos^2(e^x)) ?

The integral of ((e^x))/(cos^2(e^x)) is tan(e^x)+C

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integral of ((e^x))/(cos^2(e^x))

\int \frac{( e ^{x} )}{cos ^{2} ( e ^{x} )} d x

tan (e^{x}) + C

Solution steps

\int \frac{e ^{x}}{cos ^{2} ( e ^{x} )} d x

Rewrite using trig identities

= \int e^{x} sec^{2} (e^{x}) 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}

= tan (e^{x})

Add a constant to the solution

= tan (e^{x}) + C

What is the integral of ((e^x))/(cos^2(e^x)) ?
The integral of ((e^x))/(cos^2(e^x)) is tan(e^x)+C