integral of e^{arcsin(x)}

Lösung

\int e^{a r c s i n (x)} d x

\frac{1}{2} e^{a r c s i n (x)} x + \frac{1}{2} e^{a r c s i n (x)} - x^{2} + 1 + C

Schritte zur Lösung

\int e^{a r c s i n (x)} d x

Wende die partielle Integration an

= e^{a r c s i n (x)} x - \int \frac{e ^{a r c s i n (x)} x}{1 - x ^{2}} d x

\int \frac{e ^{a r c s i n (x)} x}{1 - x ^{2}} d x = - \frac{1}{2} e^{a r c s i n (x)} 1 - x^{2} + \frac{1}{2} e^{a r c s i n (x)} x

= e^{a r c s i n (x)} x - (- \frac{1}{2} e^{a r c s i n (x)} 1 - x^{2} + \frac{1}{2} e^{a r c s i n (x)} x)

Vereinfache

e^{a r c s i n (x)} x - (- \frac{1}{2} e^{a r c s i n (x)} 1 - x^{2} + \frac{1}{2} e^{a r c s i n (x)} x) : \frac{1}{2} e^{a r c s i n (x)} x + \frac{1}{2} e^{a r c s i n (x)} - x^{2} + 1

= \frac{1}{2} e^{a r c s i n (x)} x + \frac{1}{2} e^{a r c s i n (x)} - x^{2} + 1

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} e^{a r c s i n (x)} x + \frac{1}{2} e^{a r c s i n (x)} - x^{2} + 1 + C

t a y l or cos (π x)

\int \frac{x - 2}{x + 2} d x

t an g e n t f (x) = (x - 2) (x^{2} - 10 x + 25)

d er i v a t i v e e^{t} sin (t)

f (t) = t^{2} + 1