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\int _{122}^{328}\left(2-\left(x^{2}-4x+4\right)\right)^{2}-\left(2-0\times 5\right)^{2}\mathrm{d}x
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.
\int _{122}^{328}\left(2-x^{2}+4x-4\right)^{2}-\left(2-0\times 5\right)^{2}\mathrm{d}x
x^{2}-4x+4 teskarisini topish uchun har birining teskarisini toping.
\int _{122}^{328}\left(-2-x^{2}+4x\right)^{2}-\left(2-0\times 5\right)^{2}\mathrm{d}x
-2 olish uchun 2 dan 4 ni ayirish.
\int _{122}^{328}x^{4}-8x^{3}+20x^{2}-16x+4-\left(2-0\times 5\right)^{2}\mathrm{d}x
-2-x^{2}+4x kvadratini chiqarish.
\int _{122}^{328}x^{4}-8x^{3}+20x^{2}-16x+4-\left(2-0\right)^{2}\mathrm{d}x
0 hosil qilish uchun 0 va 5 ni ko'paytirish.
\int _{122}^{328}x^{4}-8x^{3}+20x^{2}-16x+4-2^{2}\mathrm{d}x
2 olish uchun 2 dan 0 ni ayirish.
\int _{122}^{328}x^{4}-8x^{3}+20x^{2}-16x+4-4\mathrm{d}x
2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.
\int _{122}^{328}x^{4}-8x^{3}+20x^{2}-16x\mathrm{d}x
0 olish uchun 4 dan 4 ni ayirish.
\int x^{4}-8x^{3}+20x^{2}-16x\mathrm{d}x
Avval noaniq integralni baholang.
\int x^{4}\mathrm{d}x+\int -8x^{3}\mathrm{d}x+\int 20x^{2}\mathrm{d}x+\int -16x\mathrm{d}x
Summani muddatma-muddat integratsiya qiling.
\int x^{4}\mathrm{d}x-8\int x^{3}\mathrm{d}x+20\int x^{2}\mathrm{d}x-16\int x\mathrm{d}x
Har bir shartda konstantani qavsdan tashqariga oling.
\frac{x^{5}}{5}-8\int x^{3}\mathrm{d}x+20\int x^{2}\mathrm{d}x-16\int x\mathrm{d}x
k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{4}\mathrm{d}x integralni \frac{x^{5}}{5} bilan almashtiring.
\frac{x^{5}}{5}-2x^{4}+20\int x^{2}\mathrm{d}x-16\int x\mathrm{d}x
k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring. -8 ni \frac{x^{4}}{4} marotabaga ko'paytirish.
\frac{x^{5}}{5}-2x^{4}+\frac{20x^{3}}{3}-16\int x\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. 20 ni \frac{x^{3}}{3} marotabaga ko'paytirish.
\frac{x^{5}}{5}-2x^{4}+\frac{20x^{3}}{3}-8x^{2}
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. -16 ni \frac{x^{2}}{2} marotabaga ko'paytirish.
\frac{328^{5}}{5}-2\times 328^{4}+\frac{20}{3}\times 328^{3}-8\times 328^{2}-\left(\frac{122^{5}}{5}-2\times 122^{4}+\frac{20}{3}\times 122^{3}-8\times 122^{2}\right)
Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.
\frac{10970799276608}{15}
Qisqartirish.