Issolvi ∫ 1.2x^2+16.2x+62.3 wrt x

$$\int{ 1.2 { x }^{ 2 } +16.2x+62.3 }d x$$

Evalwa

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}+С$$

Passi tas-Soluzzjonijiet

Tintegra s-somma terminu b'terminu.

$$\int \frac{6x^{2}}{5}\mathrm{d}x+\int \frac{81x}{5}\mathrm{d}x+\int 62.3\mathrm{d}x$$

Iffattura ‘l barra l-kostanti f’kull wieħed minn dawn it-termini.

$$\frac{6\int x^{2}\mathrm{d}x}{5}+\frac{81\int x\mathrm{d}x}{5}+\int 62.3\mathrm{d}x$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x^{2}\mathrm{d}x ma' \frac{x^{3}}{3}. Immultiplika 1.2 b'\frac{x^{3}}{3}.

$$\frac{2x^{3}}{5}+\frac{81\int x\mathrm{d}x}{5}+\int 62.3\mathrm{d}x$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x\mathrm{d}x ma' \frac{x^{2}}{2}. Immultiplika 16.2 b'\frac{x^{2}}{2}.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\int 62.3\mathrm{d}x$$

Sib l-integru ta' 62.3 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}$$

Jekk F\left(x\right) huwa antiderivattiv ta' f\left(x\right), allura s-sett tal-antiderivati kollha ta' f\left(x\right) jingħata minn F\left(x\right)+C. Għalhekk, żid il-kostanti ta' integrazzjoni C\in \mathrm{R} mar-riżultat.

$$\frac{2x^{3}}{5}+\frac{81x^{2}}{10}+\frac{623x}{10}+С$$

Iddifferenzja w.r.t. x

$$\frac{6x^{2}}{5}+\frac{81x}{5}+62.3$$