What is the integral of (e^{arctan(x)})/(x^2+1) ?

The integral of (e^{arctan(x)})/(x^2+1) is e^{arctan(x)}+C

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integral of (e^{arctan(x)})/(x^2+1)

\int \frac{e ^{a r c t a n (x)}}{x ^{2} + 1} d x

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

Solution steps

\int \frac{e ^{a r c t a n (x)}}{x ^{2} + 1} 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 = arctan (x)

= e^{a r c t a n (x)}

Add a constant to the solution

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

What is the integral of (e^{arctan(x)})/(x^2+1) ?
The integral of (e^{arctan(x)})/(x^2+1) is e^{arctan(x)}+C