Whakaoti i te ∫ 3x^3-x^4+2x^5/x^2 wrt x

$$\int \frac { 3 x ^ { 3 } - x ^ { 4 } + 2 x ^ { 5 } } { x ^ { 2 } } d x$$

Aromātai

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

Ngā Upane Otinga

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{3x^{3}-x^{4}+2x^{5}}{x^{2}}.

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

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

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

Me whakaroha te kīanga.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{3}\mathrm{d}x ki te \frac{x^{4}}{4}. Whakareatia 2 ki te \frac{x^{4}}{4}.

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

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 -1 ki te \frac{x^{3}}{3}.

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

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

$$\frac{x^{4}}{2}-\frac{x^{3}}{3}+\frac{3x^{2}}{2}$$

Whakarūnātia.

$$\frac{3x^{2}}{2}-\frac{x^{3}}{3}+\frac{x^{4}}{2}$$

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.

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

Kimi Pārōnaki e ai ki x

$$x\left(2x^{2}-x+3\right)$$