Whakaoti i te ∫ (3v^5-v^3/3)dv

$$\int ( 3 v ^ { 5 } - v ^ { 3 / 3 } ) d v$$

Aromātai

$$\frac{v^{6}}{2}-\frac{v^{2}}{2}+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 3v^{5}\mathrm{d}v+\int -v\mathrm{d}v$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$3\int v^{5}\mathrm{d}v-\int v\mathrm{d}v$$

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

$$\frac{v^{6}}{2}-\int v\mathrm{d}v$$

Nā te mea \int v^{k}\mathrm{d}v=\frac{v^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int v\mathrm{d}v ki te \frac{v^{2}}{2}. Whakareatia -1 ki te \frac{v^{2}}{2}.

$$\frac{v^{6}-v^{2}}{2}$$

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

$$\frac{v^{6}}{2}-\frac{v^{2}}{2}+С$$

Kimi Pārōnaki e ai ki v

$$v\left(3v^{4}-1\right)$$