integral of x^2*arccos(x)

Lösung

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

\frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{3} x^{3} arccos (x) - \int - \frac{x ^{3}}{3 1 - x ^{2}} d x

\int - \frac{x ^{3}}{3 1 - x ^{2}} d x = - \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

= \frac{1}{3} x^{3} arccos (x) - (- \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}))

Vereinfache

= \frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arccos (x) + \frac{1}{3} (\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} - 1 - x^{2}) + C

\int tan^{11} (x) sec^{2} (x) d x

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

in t e g r a l rr (θ) 2 - 4 sin (θ)

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

\int (x) (sin (x)) d x