Whakaoti i te ∫ (1/x-sinx+3) wrt x

$$\int ( \frac { 1 } { x } - \sin x + 3 ) d x$$

Aromātai

$$\ln(|x|)+\cos(x)+3x+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{1}{x}\mathrm{d}x+\int -\sin(x)\mathrm{d}x+\int 3\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int \frac{1}{x}\mathrm{d}x-\int \sin(x)\mathrm{d}x+\int 3\mathrm{d}x$$

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.

$$\ln(|x|)-\int \sin(x)\mathrm{d}x+\int 3\mathrm{d}x$$

Whakamahia te \int \sin(x)\mathrm{d}x=-\cos(x) mai i te ripanga o ngā tau tōpū pātahi kia whakaputa i te huanga. Whakareatia -1 ki te -\cos(x).

$$\ln(|x|)+\cos(x)+\int 3\mathrm{d}x$$

Kimihia te tau tōpū o 3 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\ln(|x|)+\cos(x)+3x$$

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.

$$\ln(|x|)+\cos(x)+3x+С$$

Kimi Pārōnaki e ai ki x

$$-\sin(x)+3+\frac{1}{x}$$