Réitigh ∫ (4/sqrt[3]{t}+3/t^6)dt

$$\int ( \frac { 4 } { \sqrt[ 3 ] { t } } + \frac { 3 } { t ^ { 6 } } ) d t$$

Luacháil

$$6t^{\frac{2}{3}}-\frac{3}{5t^{5}}+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int \frac{4}{\sqrt[3]{t}}\mathrm{d}t+\int \frac{3}{t^{6}}\mathrm{d}t$$

Fág an leanúnach sna téarmaí as an áireamh.

$$4\int \frac{1}{\sqrt[3]{t}}\mathrm{d}t+3\int \frac{1}{t^{6}}\mathrm{d}t$$

Athscríobh \frac{1}{\sqrt[3]{t}} mar t^{-\frac{1}{3}}. Ó \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int t^{-\frac{1}{3}}\mathrm{d}t le \frac{t^{\frac{2}{3}}}{\frac{2}{3}}. Simpligh. Méadaigh 4 faoi \frac{3t^{\frac{2}{3}}}{2}.

$$6t^{\frac{2}{3}}+3\int \frac{1}{t^{6}}\mathrm{d}t$$

Ó \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int \frac{1}{t^{6}}\mathrm{d}t le -\frac{1}{5t^{5}}. Méadaigh 3 faoi -\frac{1}{5t^{5}}.

$$6t^{\frac{2}{3}}-\frac{\frac{3}{t^{5}}}{5}$$

Simpligh.

$$6t^{\frac{2}{3}}-\frac{3}{5t^{5}}$$

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

$$6t^{\frac{2}{3}}-\frac{3}{5t^{5}}+С$$

Difreálaigh w.r.t. t

$$\frac{4}{\sqrt[3]{t}}+\frac{3}{t^{6}}$$