Whakaoti i te ∫ 5x(4-2x^2)

$$\int 5 x ( 4 - 2 x ^ { 2 } )$$

Aromātai

$$-\frac{5x^{4}}{2}+10x^{2}+С$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 5x ki te 4-2x^{2}.

$$\int 20x-10x^{3}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 20x\mathrm{d}x+\int -10x^{3}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$20\int x\mathrm{d}x-10\int x^{3}\mathrm{d}x$$

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

$$10x^{2}-10\int x^{3}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{3}\mathrm{d}x ki te \frac{x^{4}}{4}. Whakareatia -10 ki te \frac{x^{4}}{4}.

$$10x^{2}-\frac{5x^{4}}{2}$$

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.

$$10x^{2}-\frac{5x^{4}}{2}+С$$

Kimi Pārōnaki e ai ki x

$$20x-10x^{3}$$