integral of (sqrt(1-x^3))/(x^2*sqrt(x))

Lösung

\int \frac{1 - x ^{3}}{x ^{2} \cdot x} d x

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int 1 1^{4 x} d x

\int \frac{2 x}{( x - 4 ) ( x + 3 )} d x

\int t^{3} (25 + 81 t^{2})^{\frac{5}{2}} d t

\int 9 t^{2} sin (t^{3}) d t

\int sinh (\frac{x}{5}) d x