integral of (arccos(x))^2

Lösung

\int (arccos (x))^{2} d x

x arccos^{2} (x) - 2 (arccos (x) 1 - x^{2} + x) + C

Schritte zur Lösung

\int (arccos (x))^{2} d x

Vereinfache

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

Wende die partielle Integration an

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

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

= x arccos^{2} (x) - 2 (arccos (x) 1 - x^{2} + x)

Füge eine Konstante zur Lösung hinzu

= x arccos^{2} (x) - 2 (arccos (x) 1 - x^{2} + x) + C

d er i v a t i v e y = x^{2} 16 - x^{2}

\int_{0}^{\frac{π}{6}} 6 sec^{3} (x) d x

l a pl a ce t r an s f or m sin (6 (t - \frac{π}{6}))

n = 0 \sum \infty \frac{1}{( 4 n + 3 ) ^{2}}

\frac{d}{d x} ((x + 3)^{\frac{1}{2}})