Resolver ∫ frac{1/2sqrt{2}}{u-sqrt{2}}

$$\int \frac { \frac { 1 } { 2 \sqrt { 2 } } } { u - \sqrt { 2 } }$$

Ebaluatu

$$\frac{\sqrt{2}x}{4\left(u-\sqrt{2}\right)}+С$$

Ebazpidea

Aurkitu \frac{1}{2\sqrt{2}\left(u-\sqrt{2}\right)}en integrala integral arrunten taulako \int a\mathrm{d}x=ax araua erabiliz.

$$\frac{1}{2\sqrt{2}\left(u-\sqrt{2}\right)}x$$

Sinplifikatu.

$$\frac{\sqrt{2}x}{4\left(u-\sqrt{2}\right)}$$

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.

$$\frac{\sqrt{2}x}{4\left(u-\sqrt{2}\right)}+С$$

Diferentziatu x balioarekiko

$$\frac{\sqrt{2}}{4\left(u-\sqrt{2}\right)}$$