Whakaoti i te ∫ (2x^5+3/x+1/x^9) wrt x

$$\int ( 2 x ^ { 5 } + \frac { 3 } { x } + \frac { 1 } { x ^ { 9 } } ) d x$$

Aromātai

$$3\ln(|x|)+\frac{x^{6}}{3}-\frac{1}{8x^{8}}+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 2x^{5}\mathrm{d}x+\int \frac{3}{x}\mathrm{d}x+\int \frac{1}{x^{9}}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$2\int x^{5}\mathrm{d}x+3\int \frac{1}{x}\mathrm{d}x+\int \frac{1}{x^{9}}\mathrm{d}x$$

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 2 ki te \frac{x^{6}}{6}.

$$\frac{x^{6}}{3}+3\int \frac{1}{x}\mathrm{d}x+\int \frac{1}{x^{9}}\mathrm{d}x$$

Whakamahia te \int \frac{1}{x}\mathrm{d}x=\ln(|x|) mai i te ripanga o ngā tau tōpū pātahi kia whakaputa i te huanga.

$$\frac{x^{6}}{3}+3\ln(|x|)+\int \frac{1}{x^{9}}\mathrm{d}x$$

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

$$\frac{x^{6}}{3}+3\ln(|x|)-\frac{1}{8x^{8}}$$

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.

$$\frac{x^{6}}{3}+3\ln(|x|)-\frac{1}{8x^{8}}+С$$

Kimi Pārōnaki e ai ki x

$$2x^{5}+\frac{3}{x}+\frac{1}{x^{9}}$$