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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

= \int 2^{u} d u

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

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

Setze in

u = arctan (x)

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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