Whakaoti i te ∫ x(2tx^2)^2 wrt x

$$\int x ( 2 t x ^ { 2 } ) ^ { 2 } d x$$

Aromātai

$$\frac{2t^{2}x^{6}}{3}+С$$

Ngā Upane Otinga

Whakarohaina te \left(2tx^{2}\right)^{2}.

$$\int x\times 2^{2}t^{2}\left(x^{2}\right)^{2}\mathrm{d}x$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$\int x\times 2^{2}t^{2}x^{4}\mathrm{d}x$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\int x\times 4t^{2}x^{4}\mathrm{d}x$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 4 kia riro ai te 5.

$$\int x^{5}\times 4t^{2}\mathrm{d}x$$

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.

$$4t^{2}\int x^{5}\mathrm{d}x$$

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}.

$$4t^{2}\times \frac{x^{6}}{6}$$

Whakarūnātia.

$$\frac{2t^{2}x^{6}}{3}$$

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.

$$\frac{2t^{2}x^{6}}{3}+С$$

Kimi Pārōnaki e ai ki x

$$4t^{2}x^{5}$$