integral of sqrt((8-x^2)/9)

Lösung

\int \frac{8 - x ^{2}}{9} d x

\frac{1}{3} x 8 - x^{2} + \frac{4}{3} (arcsin (\frac{1}{2 2} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{2 2} x))) + C

Schritte zur Lösung

\int \frac{8 - x ^{2}}{9} d x

Wende die partielle Integration an

= \frac{1}{3} x 8 - x^{2} - \int - \frac{x ^{2}}{3 - x ^{2} + 8} d x

\int - \frac{x ^{2}}{3 - x ^{2} + 8} d x = - \frac{4}{3} (arcsin (\frac{1}{2 2} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{2 2} x)))

= \frac{1}{3} x 8 - x^{2} - (- \frac{4}{3} (arcsin (\frac{1}{2 2} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{2 2} x))))

Vereinfache

= \frac{1}{3} x 8 - x^{2} + \frac{4}{3} (arcsin (\frac{1}{2 2} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{2 2} x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x 8 - x^{2} + \frac{4}{3} (arcsin (\frac{1}{2 2} x) - \frac{1}{2} sin (2 arcsin (\frac{1}{2 2} x))) + C

x \to 2 lim (4 x - x^{2})

\frac{d}{d x} (1 - 6 x^{2})

\frac{d y}{d x} = \frac{y ^{2}}{x ^{3}}, y (1) = 1

\int \frac{x}{x 81 x ^{2} - 81} d x

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