Whakaoti i te ∫ x(9x^4-12x^2+4) wrt x

$$\int x ( 9 x ^ { 4 } - 12 x ^ { 2 } + 4 ) d x$$

Aromātai

$$\frac{3x^{6}}{2}-3x^{4}+2x^{2}+С$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 9x^{4}-12x^{2}+4.

$$\int 9x^{5}-12x^{3}+4x\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 9x^{5}\mathrm{d}x+\int -12x^{3}\mathrm{d}x+\int 4x\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$9\int x^{5}\mathrm{d}x-12\int x^{3}\mathrm{d}x+4\int x\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{5}\mathrm{d}x ki te \frac{x^{6}}{6}. Whakareatia 9 ki te \frac{x^{6}}{6}.

$$\frac{3x^{6}}{2}-12\int x^{3}\mathrm{d}x+4\int x\mathrm{d}x$$

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 -12 ki te \frac{x^{4}}{4}.

$$\frac{3x^{6}}{2}-3x^{4}+4\int x\mathrm{d}x$$

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

$$\frac{3x^{6}}{2}-3x^{4}+2x^{2}$$

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.

$$\frac{3x^{6}}{2}-3x^{4}+2x^{2}+С$$

Kimi Pārōnaki e ai ki x

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