Whakaoti i te ∫ (-7sqrt{x}+5sqrt[4]{x}) wrt x

$$\int ( - 7 \sqrt { x } + 5 \sqrt[ 4 ] { x } ) d x$$

Aromātai

$$-\frac{14x^{\frac{3}{2}}}{3}+4x^{\frac{5}{4}}+С$$

Ngā Upane Otinga

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -7\sqrt{x}\mathrm{d}x+\int 5\sqrt[4]{x}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-7\int \sqrt{x}\mathrm{d}x+5\int \sqrt[4]{x}\mathrm{d}x$$

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 -7 ki te \frac{2x^{\frac{3}{2}}}{3}.

$$-\frac{14x^{\frac{3}{2}}}{3}+5\int \sqrt[4]{x}\mathrm{d}x$$

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 5 ki te \frac{4x^{\frac{5}{4}}}{5}.

$$-\frac{14x^{\frac{3}{2}}}{3}+4x^{\frac{5}{4}}$$

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.

$$-\frac{14x^{\frac{3}{2}}}{3}+4x^{\frac{5}{4}}+С$$

Kimi Pārōnaki e ai ki x

$$-7\sqrt{x}+5\sqrt[4]{x}$$