Réitigh ∫ (3x^4+7sqrt{x}) wrt x=

$$\int ( 3 x ^ { 4 } + 7 \sqrt { x } ) d x =$$

Luacháil

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

Céimeanna Réitigh

Measc an tsuim téarma fá téarma.

$$\int 3x^{4}\mathrm{d}x+\int 7\sqrt{x}\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$3\int x^{4}\mathrm{d}x+7\int \sqrt{x}\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{4}\mathrm{d}x le \frac{x^{5}}{5}. Méadaigh 3 faoi \frac{x^{5}}{5}.

$$\frac{3x^{5}}{5}+7\int \sqrt{x}\mathrm{d}x$$

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 7 faoi \frac{2x^{\frac{3}{2}}}{3}.

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

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.

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

Difreálaigh w.r.t. x

$$3x^{4}+7\sqrt{x}$$