integral of xarccos(x)

Lösung

\int x arccos (x) d x

\frac{1}{2} x^{2} arccos (x) + \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

Schritte zur Lösung

\int x arccos (x) d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} arccos (x) - \int - \frac{x ^{2}}{2 1 - x ^{2}} d x

\int - \frac{x ^{2}}{2 1 - x ^{2}} d x = - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= \frac{1}{2} x^{2} arccos (x) - (- \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))))

Vereinfache

= \frac{1}{2} x^{2} arccos (x) + \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} arccos (x) + \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

in v erse l a pl a ce \frac{1}{s ^{2} + 2 s + 3}

\int_{2}^{9} \frac{1}{7 ( x - 2 ) ^{3}} d x

x \to - 7 - lim (\frac{1}{x ^{2} ( x + 7 )})

\frac{\partial}{\partial x} (\frac{x}{( x - 1 ) ^{2} + y ^{2}})

\int e^{\frac{1}{2}}