Datrys ∫ (4/sqrt[5]{t}+3/t^6)dt

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

Enrhifo

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

Camau Ateb

Integreiddio'r swm fesul term.

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

Ffactoreiddio allan y cysonyn ym mhob un o'r termau.

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

Ailysgrifennwch \frac{1}{\sqrt[5]{t}} fel t^{-\frac{1}{5}}. Ers \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int t^{-\frac{1}{5}}\mathrm{d}t gyda \frac{t^{\frac{4}{5}}}{\frac{4}{5}}. Symleiddio. Lluoswch 4 â \frac{5t^{\frac{4}{5}}}{4}.

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

Ers \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} ar gyfer k\neq -1, disodli \int \frac{1}{t^{6}}\mathrm{d}t gyda -\frac{1}{5t^{5}}. Lluoswch 3 â -\frac{1}{5t^{5}}.

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

Symleiddio.

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

Os yw F\left(t\right) yn integryn amhendant o f\left(t\right), yna bydd F\left(t\right)+C yn rhoi’r set o holl integrynnau amhendant f\left(t\right). Felly, ychwanegwch gysonyn yr integryn C\in \mathrm{R} at y canlyniad.

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

Gwahaniaethu w.r.t. t

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