Baholash
\frac{5x^{3}}{3}+\frac{7x^{2}}{2}-2x+С
x ga nisbatan hosilani topish
5x^{2}+7x-2
Baham ko'rish
Klipbordga nusxa olish
\int 5x^{2}\mathrm{d}x+\int 7x\mathrm{d}x+\int -2\mathrm{d}x
Summani muddatma-muddat integratsiya qiling.
5\int x^{2}\mathrm{d}x+7\int x\mathrm{d}x+\int -2\mathrm{d}x
Har bir shartda konstantani qavsdan tashqariga oling.
\frac{5x^{3}}{3}+7\int x\mathrm{d}x+\int -2\mathrm{d}x
k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring. 5 ni \frac{x^{3}}{3} marotabaga ko'paytirish.
\frac{5x^{3}}{3}+\frac{7x^{2}}{2}+\int -2\mathrm{d}x
k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. 7 ni \frac{x^{2}}{2} marotabaga ko'paytirish.
\frac{5x^{3}}{3}+\frac{7x^{2}}{2}-2x
\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -2 integralini toping.
\frac{5x^{3}}{3}+\frac{7x^{2}}{2}-2x+С
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.
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