Whakaoti i te ∫ (1-sqrt[3]{x^2})^2 wrt x

$$\int ( 1 - \sqrt[ 3 ] { x ^ { 2 } } ) ^ { 2 } d x$$

Aromātai

$$\frac{3x^{\frac{7}{3}}}{7}-\frac{6x^{\frac{5}{3}}}{5}+x+С$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(1-\sqrt[3]{x^{2}}\right)^{2}.

$$\int 1-2\sqrt[3]{x^{2}}+\left(\sqrt[3]{x^{2}}\right)^{2}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 1\mathrm{d}x+\int -2x^{\frac{2}{3}}\mathrm{d}x+\int x^{\frac{4}{3}}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 1\mathrm{d}x-2\int x^{\frac{2}{3}}\mathrm{d}x+\int x^{\frac{4}{3}}\mathrm{d}x$$

Kimihia te tau tōpū o 1 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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

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 -2 ki te \frac{3x^{\frac{5}{3}}}{5}.

$$x-\frac{6x^{\frac{5}{3}}}{5}+\int x^{\frac{4}{3}}\mathrm{d}x$$

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{4}{3}}\mathrm{d}x ki te \frac{3x^{\frac{7}{3}}}{7}.

$$x-\frac{6x^{\frac{5}{3}}}{5}+\frac{3x^{\frac{7}{3}}}{7}$$

Whakarūnātia.

$$\frac{3x^{\frac{7}{3}}}{7}-\frac{6x^{\frac{5}{3}}}{5}+x$$

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.

$$\frac{3x^{\frac{7}{3}}}{7}-\frac{6x^{\frac{5}{3}}}{5}+x+С$$

Kimi Pārōnaki e ai ki x

$$\left(x^{\frac{2}{3}}-1\right)^{2}$$