integral of e^{arccos(x)}

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 2 x - \frac{1}{x ^{2}} d x

\int 2^{x} + x^{2} d x

\frac{\partial}{\partial z} (yz - ln (x + z))

x \to - \infty lim (7)

\frac{d}{d x} (\frac{x ^{3}}{2 - x ^{2}})