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

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

Aromātai

$$\frac{6x^{\frac{5}{2}}}{5}+\frac{3x^{\frac{7}{3}}}{7}+\frac{2x^{\frac{3}{2}}}{3}+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

Tuhia anō te \sqrt{x} hei x^{\frac{1}{2}}. 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{1}{2}}\mathrm{d}x ki te \frac{x^{\frac{3}{2}}}{\frac{3}{2}}. Whakarūnātia.

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

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}.

$$\frac{2x^{\frac{3}{2}}}{3}+\frac{3x^{\frac{7}{3}}}{7}+3\int x^{\frac{3}{2}}\mathrm{d}x$$

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{3}{2}}\mathrm{d}x ki te \frac{2x^{\frac{5}{2}}}{5}. Whakareatia 3 ki te \frac{2x^{\frac{5}{2}}}{5}.

$$\frac{2x^{\frac{3}{2}}}{3}+\frac{3x^{\frac{7}{3}}}{7}+\frac{6x^{\frac{5}{2}}}{5}$$

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.

$$\frac{2x^{\frac{3}{2}}}{3}+\frac{3x^{\frac{7}{3}}}{7}+\frac{6x^{\frac{5}{2}}}{5}+С$$

Kimi Pārōnaki e ai ki x

$$\sqrt{x}\left(3x+x^{\frac{5}{6}}+1\right)$$