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

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

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

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

\frac{2 ^{a r c t a n (x)}}{ln ( 2 )} + C

Solution steps

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

Apply u-substitution

: \int 2^{u} d u

= \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = arctan (x)

= \frac{2 ^{a r c t a n (x)}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{a r c t a n (x)}}{ln ( 2 )} + C

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