integral of ((8x-5)/(\sqrt[3]{x)})

Lösung

\int (\frac{8 x - 5}{3 x}) d x

\frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{8 x - 5}{3 x} d x

Multipliziere aus

\frac{8 x - 5}{3 x} : 8 x^{\frac{2}{3}} - \frac{5}{3 x}

= \int 8 x^{\frac{2}{3}} - \frac{5}{3 x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 8 x^{\frac{2}{3}} d x - \int \frac{5}{3 x} d x

\int 8 x^{\frac{2}{3}} d x = \frac{24}{5} x^{\frac{5}{3}}

\int \frac{5}{3 x} d x = \frac{15}{2} x^{\frac{2}{3}}

= \frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}} + C

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

in v erse l a pl a ce \frac{1}{( s + 20 ) [ ( s + 2 ) ^{2} + 1 ]}

n = 0 \sum \infty \frac{3 ^{n}}{1000}

\frac{d y}{d x} = x^{2} y

\frac{d}{d x} (\frac{4 x - 4 1 + x}{x ^{2} - 1})