Whakaoti i te ∫ (9/sqrt[4]{t}+4/t^7)dt

$$\int ( \frac { 9 } { \sqrt[ 4 ] { t } } + \frac { 4 } { t ^ { 7 } } ) d t$$

Aromātai

$$12t^{\frac{3}{4}}-\frac{2}{3t^{6}}+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{9}{\sqrt[4]{t}}\mathrm{d}t+\int \frac{4}{t^{7}}\mathrm{d}t$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$9\int \frac{1}{\sqrt[4]{t}}\mathrm{d}t+4\int \frac{1}{t^{7}}\mathrm{d}t$$

Tuhia anō te \frac{1}{\sqrt[4]{t}} hei t^{-\frac{1}{4}}. 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}{4}}\mathrm{d}t ki te \frac{t^{\frac{3}{4}}}{\frac{3}{4}}. Whakarūnātia. Whakareatia 9 ki te \frac{4t^{\frac{3}{4}}}{3}.

$$12t^{\frac{3}{4}}+4\int \frac{1}{t^{7}}\mathrm{d}t$$

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^{7}}\mathrm{d}t ki te -\frac{1}{6t^{6}}. Whakareatia 4 ki te -\frac{1}{6t^{6}}.

$$12t^{\frac{3}{4}}-\frac{2}{3t^{6}}$$

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.

$$12t^{\frac{3}{4}}-\frac{2}{3t^{6}}+С$$

Kimi Pārōnaki e ai ki t

$$\frac{9}{\sqrt[4]{t}}+\frac{4}{t^{7}}$$