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

$$\int ( 2 \sqrt { x } - \sqrt[ 4 ] { x } ) d x$$

Aromātai

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

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 2\sqrt{x}\mathrm{d}x+\int -\sqrt[4]{x}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$2\int \sqrt{x}\mathrm{d}x-\int \sqrt[4]{x}\mathrm{d}x$$

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

$$\frac{4x^{\frac{3}{2}}}{3}-\int \sqrt[4]{x}\mathrm{d}x$$

Tuhia anō te \sqrt[4]{x} hei x^{\frac{1}{4}}. 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}{4}}\mathrm{d}x ki te \frac{x^{\frac{5}{4}}}{\frac{5}{4}}. Whakarūnātia. Whakareatia -1 ki te \frac{4x^{\frac{5}{4}}}{5}.

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

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.

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

Kimi Pārōnaki e ai ki x

$$2\sqrt{x}-\sqrt[4]{x}$$