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

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

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

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

tan (e^{x}) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{e ^{x}}{cos ^{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

y^{^{''}} + 25 y = 20 sin (5 x)

e^{x - y} d x + e^{y - x} d y = 0

d er i v a t i v e f (x^{2})

\frac{\partial}{\partial x} (\frac{1}{e ^{x}})

9 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0

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