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

= \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

\int \frac{( 1 - x ) ^{2}}{x} d x

\int \frac{x ^{3} + 1}{( x ^{2} + 1 ) ^{2}} d x

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

\int \frac{1}{1 + x - x ^{2}} d x

\int \frac{1 + cos ^{2} ( x )}{1 + cos ( 2 x )} d x

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