Whakaoti i te ∫ (4x^7+4x+4)(28x^6+4) wrt x

$$\int ( 4 x ^ { 7 } + 4 x + 4 ) ( 28 x ^ { 6 } + 4 ) d x$$

Aromātai

$$8x^{14}+16x^{8}+16x^{7}+8x^{2}+16x+С$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x^{7}+4x+4 ki te 28x^{6}+4 ka whakakotahi i ngā kupu rite.

$$\int 112x^{13}+128x^{7}+16x+112x^{6}+16\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 112x^{13}\mathrm{d}x+\int 128x^{7}\mathrm{d}x+\int 16x\mathrm{d}x+\int 112x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$112\int x^{13}\mathrm{d}x+128\int x^{7}\mathrm{d}x+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{13}\mathrm{d}x ki te \frac{x^{14}}{14}. Whakareatia 112 ki te \frac{x^{14}}{14}.

$$8x^{14}+128\int x^{7}\mathrm{d}x+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{7}\mathrm{d}x ki te \frac{x^{8}}{8}. Whakareatia 128 ki te \frac{x^{8}}{8}.

$$8x^{14}+16x^{8}+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

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

$$8x^{14}+16x^{8}+8x^{2}+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{6}\mathrm{d}x ki te \frac{x^{7}}{7}. Whakareatia 112 ki te \frac{x^{7}}{7}.

$$8x^{14}+16x^{8}+8x^{2}+16x^{7}+\int 16\mathrm{d}x$$

Kimihia te tau tōpū o 16 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$8x^{14}+16x^{8}+8x^{2}+16x^{7}+16x$$

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.

$$8x^{14}+16x^{8}+16x^{7}+8x^{2}+16x+С$$

Kimi Pārōnaki e ai ki x

$$16\left(7x^{6}+1\right)\left(x^{7}+x+1\right)$$