Whakaoti i te ∫ (3x+5)(7x-2) wrt x

$$\int ( 3 x + 5 ) ( 7 x - 2 ) d x$$

Aromātai

$$7x^{3}+\frac{29x^{2}}{2}-10x+С$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3x+5 ki ia tau o 7x-2.

$$\int 21x^{2}-6x+35x-10\mathrm{d}x$$

Pahekotia te -6x me 35x, ka 29x.

$$\int 21x^{2}+29x-10\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 21x^{2}\mathrm{d}x+\int 29x\mathrm{d}x+\int -10\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$21\int x^{2}\mathrm{d}x+29\int x\mathrm{d}x+\int -10\mathrm{d}x$$

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

$$7x^{3}+29\int x\mathrm{d}x+\int -10\mathrm{d}x$$

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

$$7x^{3}+\frac{29x^{2}}{2}+\int -10\mathrm{d}x$$

Kimihia te tau tōpū o -10 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$7x^{3}+\frac{29x^{2}}{2}-10x$$

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.

$$7x^{3}+\frac{29x^{2}}{2}-10x+С$$

Kimi Pārōnaki e ai ki x

$$\left(7x-2\right)\left(3x+5\right)$$