Whakaoti i te ∫ (4x^5-3sqrt[3]{x^2}+3) wrt x

$$\int ( 4 x ^ { 5 } - 3 \sqrt[ 3 ] { x ^ { 2 } } + 3 ) d x$$

Aromātai

$$\frac{2x^{6}}{3}-\frac{9x^{\frac{5}{3}}}{5}+3x+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 4x^{5}\mathrm{d}x+\int -3x^{\frac{2}{3}}\mathrm{d}x+\int 3\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$4\int x^{5}\mathrm{d}x-3\int x^{\frac{2}{3}}\mathrm{d}x+\int 3\mathrm{d}x$$

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

$$\frac{2x^{6}}{3}-3\int x^{\frac{2}{3}}\mathrm{d}x+\int 3\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{\frac{2}{3}}\mathrm{d}x ki te \frac{3x^{\frac{5}{3}}}{5}. Whakareatia -3 ki te \frac{3x^{\frac{5}{3}}}{5}.

$$\frac{2x^{6}}{3}-\frac{9x^{\frac{5}{3}}}{5}+\int 3\mathrm{d}x$$

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.

$$\frac{2x^{6}}{3}-\frac{9x^{\frac{5}{3}}}{5}+3x$$

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.

$$\frac{2x^{6}}{3}-\frac{9x^{\frac{5}{3}}}{5}+3x+С$$

Kimi Pārōnaki e ai ki x

$$4x^{5}-3x^{\frac{2}{3}}+3$$