Whakaoti i te ∫ 18x^3+33x^2-40x-75/3x+5 wrt x

$$\int \frac { 18 x ^ { 3 } + 33 x ^ { 2 } - 40 x - 75 } { 3 x + 5 } d x$$

Aromātai

$$2x^{3}+\frac{x^{2}}{2}-15x+С$$

Ngā Upane Otinga

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{18x^{3}+33x^{2}-40x-75}{3x+5}.

$$\int \frac{\left(2x-3\right)\left(3x+5\right)^{2}}{3x+5}\mathrm{d}x$$

Me whakakore tahi te 3x+5 i te taurunga me te tauraro.

$$\int \left(2x-3\right)\left(3x+5\right)\mathrm{d}x$$

Me whakaroha te kīanga.

$$\int 6x^{2}+x-15\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 6x^{2}\mathrm{d}x+\int x\mathrm{d}x+\int -15\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$6\int x^{2}\mathrm{d}x+\int x\mathrm{d}x+\int -15\mathrm{d}x$$

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}.

$$2x^{3}+\int x\mathrm{d}x+\int -15\mathrm{d}x$$

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}.

$$2x^{3}+\frac{x^{2}}{2}+\int -15\mathrm{d}x$$

Kimihia te tau tōpū o -15 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$2x^{3}+\frac{x^{2}}{2}-15x$$

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.

$$-15x+\frac{x^{2}}{2}+2x^{3}+С$$

Kimi Pārōnaki e ai ki x

$$6x^{2}+x-15$$