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

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

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integral of e^{tan(θ)}sec^2(θ)

\int e^{t a n (θ)} sec^{2} (θ) d θ

e^{t a n (θ)} + C

Solution steps

\int e^{t a n (θ)} sec^{2} (θ) d θ

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 (θ)

= e^{t a n (θ)}

Add a constant to the solution

= e^{t a n (θ)} + C

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