Réitigh ∫ 6 wrt x/sqrt[3]{x}

$$\int \frac { 6 d x } { \sqrt[ 3 ] { x } }$$

Luacháil

$$9x^{\frac{2}{3}}+С$$

Céimeanna Réitigh

Fág an úsáid leanúnach do\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x as an áireamh.

$$6\int \frac{1}{\sqrt[3]{x}}\mathrm{d}x$$

Athscríobh \frac{1}{\sqrt[3]{x}} mar x^{-\frac{1}{3}}. Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{-\frac{1}{3}}\mathrm{d}x le \frac{x^{\frac{2}{3}}}{\frac{2}{3}}. Simpligh. Méadaigh 6 faoi \frac{3x^{\frac{2}{3}}}{2}.

$$9x^{\frac{2}{3}}$$

Má tá F\left(x\right) mar frithdhíorthach do f\left(x\right), beidh tacar do frithdhíorthach uile do f\left(x\right) a thabhairt ag F\left(x\right)+C. Mar sin de, cur an comhtháthú leanúnach C\in \mathrm{R} don toradh.

$$9x^{\frac{2}{3}}+С$$

Difreálaigh w.r.t. x

$$\frac{6}{\sqrt[3]{x}}$$