Whakaoti i te ∫ 5x*(-2xy)+2x^2*(-2y)+7*(2x^2y)=

$$\int 5 x \cdot ( - 2 x y ) + 2 x ^ { 2 } \cdot ( - 2 y ) + 7 \cdot ( 2 x ^ { 2 } y ) =$$

Aromātai

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Ngā Upane Otinga

Whakareatia te x ki te x, ka x^{2}.

$$\int 5x^{2}\left(-2\right)y+2x^{2}\left(-2\right)y+7\times 2x^{2}y\mathrm{d}x$$

Whakareatia te 5 ki te -2, ka -10.

$$\int -10x^{2}y+2x^{2}\left(-2\right)y+7\times 2x^{2}y\mathrm{d}x$$

Whakareatia te 2 ki te -2, ka -4.

$$\int -10x^{2}y-4x^{2}y+7\times 2x^{2}y\mathrm{d}x$$

Pahekotia te -10x^{2}y me -4x^{2}y, ka -14x^{2}y.

$$\int -14x^{2}y+7\times 2x^{2}y\mathrm{d}x$$

Whakareatia te 7 ki te 2, ka 14.

$$\int -14x^{2}y+14x^{2}y\mathrm{d}x$$

Pahekotia te -14x^{2}y me 14x^{2}y, ka 0.

$$\int 0\mathrm{d}x$$

Kimihia te tau tōpū o 0 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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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.

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Kimi Pārōnaki e ai ki x

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