Whakaoti i te ∫ (4/sqrt[5]{t}+3/t^6)dt

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

Aromātai

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

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

Tuhia anō te \frac{1}{\sqrt[5]{t}} hei t^{-\frac{1}{5}}. Nā te mea \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int t^{-\frac{1}{5}}\mathrm{d}t ki te \frac{t^{\frac{4}{5}}}{\frac{4}{5}}. Whakarūnātia. Whakareatia 4 ki te \frac{5t^{\frac{4}{5}}}{4}.

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

Nā te mea \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int \frac{1}{t^{6}}\mathrm{d}t ki te -\frac{1}{5t^{5}}. Whakareatia 3 ki te -\frac{1}{5t^{5}}.

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

Whakarūnātia.

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

Mēnā ko F\left(t\right) he pārōnaki kōaro o f\left(t\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(t\right) ka whakaaturia e F\left(t\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.

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

Kimi Pārōnaki e ai ki t

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