Whakaoti i te ∫ -3x^2left(4x^3+4right)^3 wrt x

$$\int{ -3 { x }^{ 2 } { \left(4 { x }^{ 3 } +4 \right) }^{ 3 } }d x$$

Aromātai

$$С-64x^{3}-96x^{6}-64x^{9}-16x^{12}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} hei whakaroha \left(4x^{3}+4\right)^{3}.

$$\int -3x^{2}\left(64\left(x^{3}\right)^{3}+192\left(x^{3}\right)^{2}+192x^{3}+64\right)\mathrm{d}x$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 3 kia riro ai te 9.

$$\int -3x^{2}\left(64x^{9}+192\left(x^{3}\right)^{2}+192x^{3}+64\right)\mathrm{d}x$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

$$\int -3x^{2}\left(64x^{9}+192x^{6}+192x^{3}+64\right)\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3x^{2} ki te 64x^{9}+192x^{6}+192x^{3}+64.

$$\int -192x^{11}-576x^{8}-576x^{5}-192x^{2}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -192x^{11}\mathrm{d}x+\int -576x^{8}\mathrm{d}x+\int -576x^{5}\mathrm{d}x+\int -192x^{2}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-192\int x^{11}\mathrm{d}x-576\int x^{8}\mathrm{d}x-576\int x^{5}\mathrm{d}x-192\int x^{2}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{11}\mathrm{d}x ki te \frac{x^{12}}{12}. Whakareatia -192 ki te \frac{x^{12}}{12}.

$$-16x^{12}-576\int x^{8}\mathrm{d}x-576\int x^{5}\mathrm{d}x-192\int x^{2}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{8}\mathrm{d}x ki te \frac{x^{9}}{9}. Whakareatia -576 ki te \frac{x^{9}}{9}.

$$-16x^{12}-64x^{9}-576\int x^{5}\mathrm{d}x-192\int x^{2}\mathrm{d}x$$

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 -576 ki te \frac{x^{6}}{6}.

$$-16x^{12}-64x^{9}-96x^{6}-192\int x^{2}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{2}\mathrm{d}x ki te \frac{x^{3}}{3}. Whakareatia -192 ki te \frac{x^{3}}{3}.

$$-16x^{12}-64x^{9}-96x^{6}-64x^{3}$$

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.

$$-64x^{3}-96x^{6}-64x^{9}-16x^{12}+С$$

Kimi Pārōnaki e ai ki x

$$-192x^{2}\left(x^{3}+1\right)^{3}$$