Réitigh ∫ (4/sqrt[5]{t}+3/t^6)dt

$$\int ( \frac { 4 } { \sqrt[ 5 ] { t } } + \frac { 3 } { t ^ { 6 } } ) d t$$

Luacháil

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}+С$$

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int \frac{4}{\sqrt[5]{t}}\mathrm{d}t+\int \frac{3}{t^{6}}\mathrm{d}t$$

Fág an leanúnach sna téarmaí as an áireamh.

$$4\int \frac{1}{\sqrt[5]{t}}\mathrm{d}t+3\int \frac{1}{t^{6}}\mathrm{d}t$$

Athscríobh \frac{1}{\sqrt[5]{t}} mar t^{-\frac{1}{5}}. Ó \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int t^{-\frac{1}{5}}\mathrm{d}t le \frac{t^{\frac{4}{5}}}{\frac{4}{5}}. Simpligh. Méadaigh 4 faoi \frac{5t^{\frac{4}{5}}}{4}.

$$5t^{\frac{4}{5}}+3\int \frac{1}{t^{6}}\mathrm{d}t$$

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}}.

$$5t^{\frac{4}{5}}-\frac{\frac{3}{t^{5}}}{5}$$

Simpligh.

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}$$

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.

$$5t^{\frac{4}{5}}-\frac{3}{5t^{5}}+С$$

Difreálaigh w.r.t. t

$$\frac{4}{\sqrt[5]{t}}+\frac{3}{t^{6}}$$