Whakaoti i te ∫ 12x^2+16*2x+62*3 wrt x

$$\int 12 x ^ { 2 } + 16 \cdot 2 x + 62 \cdot 3 d x$$

Aromātai

$$4x^{3}+16x^{2}+186x+С$$

Ngā Upane Otinga

Mahia ngā whakarea.

$$\int 12x^{2}+32x+186\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 12x^{2}\mathrm{d}x+\int 32x\mathrm{d}x+\int 186\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$12\int x^{2}\mathrm{d}x+32\int x\mathrm{d}x+\int 186\mathrm{d}x$$

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 12 ki te \frac{x^{3}}{3}.

$$4x^{3}+32\int x\mathrm{d}x+\int 186\mathrm{d}x$$

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 32 ki te \frac{x^{2}}{2}.

$$4x^{3}+16x^{2}+\int 186\mathrm{d}x$$

Kimihia te tau tōpū o 186 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$4x^{3}+16x^{2}+186x$$

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.

$$4x^{3}+16x^{2}+186x+С$$

Kimi Pārōnaki e ai ki x

$$12x^{2}+32x+186$$