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

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

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

\int e^{s e c (x)} sec (x) tan (x) d x

e^{s e c (x)} + C

Solution steps

\int e^{s e c (x)} sec (x) tan (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 = sec (x)

= e^{s e c (x)}

Add a constant to the solution

= e^{s e c (x)} + C

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