∫ (from -9 to 45) of 5x+8585+68*{(e)^15 wrt x eching

$$\int_{ -9 }^{ 45 } 5x+8585+68 \times {(e)^{ 15 }} d x$$

Baholash

$$3672e^{15}+468450\approx 12004300241,717580795$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 5x+8585+68e^{15}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 5x\mathrm{d}x+\int 8585\mathrm{d}x+\int 68e^{15}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$5\int x\mathrm{d}x+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

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. 5 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$\frac{5x^{2}}{2}+\int 8585\mathrm{d}x+68\int e^{15}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 8585 integralini toping.

$$\frac{5x^{2}}{2}+8585x+68\int e^{15}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, e^{15} integralini toping.

$$\frac{5x^{2}}{2}+8585x+68e^{15}x$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$\frac{5}{2}\times 45^{2}+8585\times 45+68e^{15}\times 45-\left(\frac{5}{2}\left(-9\right)^{2}+8585\left(-9\right)+68e^{15}\left(-9\right)\right)$$

Qisqartirish.

$$468450+3672e^{15}$$