∫ frac{1/2sqrt{2}}{u-sqrt{2}} eching

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

Baholash

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

Yechim qadamlari

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \frac{1}{2\sqrt{2}\left(u-\sqrt{2}\right)} integralini toping.

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

Qisqartirish.

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

Агар F\left(x\right)f\left(x\right) ning dastlabki holati boʻlsa, u holatda f\left(x\right) ning barcha dastlabki holatlari toʻplami F\left(x\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

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

x ga nisbatan hosilani topish

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