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

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

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integral of sec^2(x)(e^{tan(x)})

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

e^{t a n (x)} + C

Solution steps

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

Apply u-substitution

: \int e^{u} d u

= \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= e^{u}

Substitute back

u = tan (x)

= e^{t a n (x)}

Add a constant to the solution

= e^{t a n (x)} + C

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