Whakaoti i te ∫ x^6(5x-6) wrt x

$$\int x ^ { 6 } ( 5 x - 6 ) d x$$

Aromātai

$$\frac{5x^{8}}{8}-\frac{6x^{7}}{7}+С$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te x^{6} ki te 5x-6.

$$\int 5x^{7}-6x^{6}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 5x^{7}\mathrm{d}x+\int -6x^{6}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$5\int x^{7}\mathrm{d}x-6\int x^{6}\mathrm{d}x$$

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 5 ki te \frac{x^{8}}{8}.

$$\frac{5x^{8}}{8}-6\int x^{6}\mathrm{d}x$$

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 -6 ki te \frac{x^{7}}{7}.

$$\frac{5x^{8}}{8}-\frac{6x^{7}}{7}$$

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.

$$\frac{5x^{8}}{8}-\frac{6x^{7}}{7}+С$$

Kimi Pārōnaki e ai ki x

$$\left(5x-6\right)x^{6}$$