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

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

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

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

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

Solution steps

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

Apply u-substitution

= \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

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