Whakaoti i te ∫ x^2dive^2x wrt x

$$\int{ { x }^{ 2 } \div { e }^{ 2 } x }d x$$

Aromātai

$$\frac{x^{4}}{4e^{2}}+С$$

Ngā Upane Otinga

Tuhia te \frac{x^{2}}{e^{2}}x hei hautanga kotahi.

$$\int \frac{x^{2}x}{e^{2}}\mathrm{d}x$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$\int \frac{x^{3}}{e^{2}}\mathrm{d}x$$

Whakatauwehetia te pūmau mā te whakamahi i te \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{\int x^{3}\mathrm{d}x}{e^{2}}$$

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}.

$$\frac{x^{4}}{4e^{2}}$$

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.

$$\frac{x^{4}}{4e^{2}}+С$$

Kimi Pārōnaki e ai ki x

$$\frac{x^{3}}{e^{2}}$$