Réitigh ∫ x^2(20x^7-7x^4+1) wrt x

$$\int x ^ { 2 } ( 20 x ^ { 7 } - 7 x ^ { 4 } + 1 ) d x$$

Luacháil

$$2x^{10}-x^{7}+\frac{x^{3}}{3}+С$$

Céimeanna Réitigh

Úsáid an t-airí dáileach chun x^{2} a mhéadú faoi 20x^{7}-7x^{4}+1.

$$\int 20x^{9}-7x^{6}+x^{2}\mathrm{d}x$$

Measc an tsuim téarma fá téarma.

$$\int 20x^{9}\mathrm{d}x+\int -7x^{6}\mathrm{d}x+\int x^{2}\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$20\int x^{9}\mathrm{d}x-7\int x^{6}\mathrm{d}x+\int x^{2}\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{9}\mathrm{d}x le \frac{x^{10}}{10}. Méadaigh 20 faoi \frac{x^{10}}{10}.

$$2x^{10}-7\int x^{6}\mathrm{d}x+\int x^{2}\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{6}\mathrm{d}x le \frac{x^{7}}{7}. Méadaigh -7 faoi \frac{x^{7}}{7}.

$$2x^{10}-x^{7}+\int x^{2}\mathrm{d}x$$

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

$$2x^{10}-x^{7}+\frac{x^{3}}{3}$$

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.

$$2x^{10}-x^{7}+\frac{x^{3}}{3}+С$$

Difreálaigh w.r.t. x

$$20x^{9}-7x^{6}+x^{2}$$