integral of \sqrt[3]{ax^2}

Lösung

\int 3 a x^{2} d x

x 3 a x^{2} - \frac{2 3 a x ^{\frac{5}{3}}}{5} + C

Schritte zur Lösung

\int 3 a x^{2} d x

Wende die partielle Integration an

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

\int \frac{2 a ^{\frac{1}{3}} x ^{2}}{3 ( x ^{2} ) ^{\frac{2}{3}}} d x = \frac{2 a ^{\frac{1}{3}} x ^{\frac{5}{3}}}{5}

= x 3 a x^{2} - \frac{2 a ^{\frac{1}{3}} x ^{\frac{5}{3}}}{5}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= x 3 a x^{2} - \frac{2 3 a x ^{\frac{5}{3}}}{5}

Füge eine Konstante zur Lösung hinzu

= x 3 a x^{2} - \frac{2 3 a x ^{\frac{5}{3}}}{5} + C

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

x \to \infty lim (tan (\frac{7}{x}))

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

\int (e^{x} x) d x

x \to \infty lim (\frac{( e ^{2 x} - 8 - 19 x )}{( 19 x ) ^{2}})