Whakaoti i te ∫ (6x^2+8x+3) wrt x

$$\int ( 6 x ^ { 2 } + 8 x + 3 ) d x$$

Aromātai

$$2x^{3}+4x^{2}+3x+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 6x^{2}\mathrm{d}x+\int 8x\mathrm{d}x+\int 3\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$6\int x^{2}\mathrm{d}x+8\int x\mathrm{d}x+\int 3\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{2}\mathrm{d}x ki te \frac{x^{3}}{3}. Whakareatia 6 ki te \frac{x^{3}}{3}.

$$2x^{3}+8\int x\mathrm{d}x+\int 3\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia 8 ki te \frac{x^{2}}{2}.

$$2x^{3}+4x^{2}+\int 3\mathrm{d}x$$

Kimihia te tau tōpū o 3 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$2x^{3}+4x^{2}+3x$$

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

$$2x^{3}+4x^{2}+3x+С$$

Kimi Pārōnaki e ai ki x

$$6x^{2}+8x+3$$