∫ wrt x/sqrt[3]{8x^2} eching

$$\int \frac { d x } { \sqrt[ 3 ] { 8 x ^ { 2 } } }$$

Baholash

$$\frac{3\sqrt[3]{x}}{2}+С$$

Yechim qadamlari

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$\frac{\int \frac{1}{\sqrt[3]{x^{2}}}\mathrm{d}x}{\sqrt[3]{8}}$$

\frac{1}{x^{\frac{2}{3}}} ni x^{-\frac{2}{3}} sifatida qaytadan yozish. k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{-\frac{2}{3}}\mathrm{d}x integralni \frac{x^{\frac{1}{3}}}{\frac{1}{3}} bilan almashtiring. Soddalashtiring va eksponensialdan ildiz shaklga aylantiring.

$$\frac{3\sqrt[3]{x}}{\sqrt[3]{8}}$$

Qisqartirish.

$$\frac{3\sqrt[3]{x}}{2}$$

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.

$$\frac{3\sqrt[3]{x}}{2}+С$$

x ga nisbatan hosilani topish

$$\frac{1}{2x^{\frac{2}{3}}}$$