∫ left(2*xright)^22 wrt x eching

$$\int{ { \left(2 \times x \right) }^{ 22 } }d x$$

Baholash

$$\frac{4194304x^{23}}{23}+С$$

Yechim qadamlari

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

$$2^{22}\int x^{22}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{22}\mathrm{d}x integralni \frac{x^{23}}{23} bilan almashtiring.

$$2^{22}\times \frac{x^{23}}{23}$$

Qisqartirish.

$$\frac{4194304x^{23}}{23}$$

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.

$$\frac{4194304x^{23}}{23}+С$$

x ga nisbatan hosilani topish

$$4194304x^{22}$$