Resolver ∫ 1.2x^2+16.2x+62.3 wrt x

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

Ebaluatu

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

Ebazpidea

Integratu gehiketa gaiz gai.

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

Deskonposatu konstantea gaika.

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

Baldin k\neq -1rentzat \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1}, ordeztu \int x^{2}\mathrm{d}x \frac{x^{3}}{3}rekin. Egin 1.2 bider \frac{x^{3}}{3}.

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

Baldin k\neq -1rentzat \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1}, ordeztu \int x\mathrm{d}x \frac{x^{2}}{2}rekin. Egin 16.2 bider \frac{x^{2}}{2}.

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

Aurkitu 62.3en integrala integral arrunten taulako \int a\mathrm{d}x=ax araua erabiliz.

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

F\left(x\right) f\left(x\right)ren jatorrizkoa bada, orduan f\left(x\right)ren jatorrizko guztien multzoa ematen du F\left(x\right)+Ck. Beraz, gehitu C\in \mathrm{R} integrazio-konstantea emaitzari.

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

Diferentziatu x balioarekiko

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