Whakaoti i te ∫ (-m+8m^3-8m^5)dm

$$\int ( - m + 8 m ^ { 3 } - 8 m ^ { 5 } ) d m$$

Aromātai

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

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -m\mathrm{d}m+\int 8m^{3}\mathrm{d}m+\int -8m^{5}\mathrm{d}m$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-\int m\mathrm{d}m+8\int m^{3}\mathrm{d}m-8\int m^{5}\mathrm{d}m$$

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

$$-\frac{m^{2}}{2}+8\int m^{3}\mathrm{d}m-8\int m^{5}\mathrm{d}m$$

Nā te mea \int m^{k}\mathrm{d}m=\frac{m^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int m^{3}\mathrm{d}m ki te \frac{m^{4}}{4}. Whakareatia 8 ki te \frac{m^{4}}{4}.

$$-\frac{m^{2}}{2}+2m^{4}-8\int m^{5}\mathrm{d}m$$

Nā te mea \int m^{k}\mathrm{d}m=\frac{m^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int m^{5}\mathrm{d}m ki te \frac{m^{6}}{6}. Whakareatia -8 ki te \frac{m^{6}}{6}.

$$-\frac{m^{2}}{2}+2m^{4}-\frac{4m^{6}}{3}$$

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

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

Kimi Pārōnaki e ai ki m

$$m\left(-8m^{4}+8m^{2}-1\right)$$