Réitigh ∫ (4x^7+4x+4)(28x^6+4) wrt x

$$\int ( 4 x ^ { 7 } + 4 x + 4 ) ( 28 x ^ { 6 } + 4 ) d x$$

Luacháil

$$8x^{14}+16x^{8}+16x^{7}+8x^{2}+16x+С$$

Céimeanna Réitigh

Úsáid an t-airí dáileach chun 4x^{7}+4x+4 a mhéadú faoi 28x^{6}+4 agus chun téarmaí comhchosúla a chumasc.

$$\int 112x^{13}+128x^{7}+16x+112x^{6}+16\mathrm{d}x$$

Measc an tsuim téarma fá téarma.

$$\int 112x^{13}\mathrm{d}x+\int 128x^{7}\mathrm{d}x+\int 16x\mathrm{d}x+\int 112x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Fág an leanúnach sna téarmaí as an áireamh.

$$112\int x^{13}\mathrm{d}x+128\int x^{7}\mathrm{d}x+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{13}\mathrm{d}x le \frac{x^{14}}{14}. Méadaigh 112 faoi \frac{x^{14}}{14}.

$$8x^{14}+128\int x^{7}\mathrm{d}x+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x^{7}\mathrm{d}x le \frac{x^{8}}{8}. Méadaigh 128 faoi \frac{x^{8}}{8}.

$$8x^{14}+16x^{8}+16\int x\mathrm{d}x+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

Ó \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} fá choinne k\neq -1, athchuir \int x\mathrm{d}x le \frac{x^{2}}{2}. Méadaigh 16 faoi \frac{x^{2}}{2}.

$$8x^{14}+16x^{8}+8x^{2}+112\int x^{6}\mathrm{d}x+\int 16\mathrm{d}x$$

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 112 faoi \frac{x^{7}}{7}.

$$8x^{14}+16x^{8}+8x^{2}+16x^{7}+\int 16\mathrm{d}x$$

Aimsigh suimeálaithe do 16 ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}x=ax.

$$8x^{14}+16x^{8}+8x^{2}+16x^{7}+16x$$

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.

$$8x^{14}+16x^{8}+16x^{7}+8x^{2}+16x+С$$

Difreálaigh w.r.t. x

$$16\left(7x^{6}+1\right)\left(x^{7}+x+1\right)$$