Réitigh ∫ (2sqrt{x}-sqrt[4]{x}) wrt x

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

Luacháil

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

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

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

Fág an leanúnach sna téarmaí as an áireamh.

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

Athscríobh \sqrt{x} mar x^{\frac{1}{2}}. Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{\frac{1}{2}}\mathrm{d}x le \frac{x^{\frac{3}{2}}}{\frac{3}{2}}. Simpligh. Méadaigh 2 faoi \frac{2x^{\frac{3}{2}}}{3}.

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

Athscríobh \sqrt[4]{x} mar x^{\frac{1}{4}}. Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{\frac{1}{4}}\mathrm{d}x le \frac{x^{\frac{5}{4}}}{\frac{5}{4}}. Simpligh. Méadaigh -1 faoi \frac{4x^{\frac{5}{4}}}{5}.

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

Má tá F\left(x\right) mar frithdhíorthach do f\left(x\right), beidh tacar do frithdhíorthach uile do f\left(x\right) a thabhairt ag F\left(x\right)+C. Mar sin de, cur an comhtháthú leanúnach C\in \mathrm{R} don toradh.

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

Difreálaigh w.r.t. x

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