Ответ:
[tex]f(x) = 8 {x}^{7} - \frac{3}{2 \sqrt{x} } \\ F(x) = \int \: f(x) dx = \int(8 {x}^{7} - \frac{3}{2 \sqrt{x} } )dx = \\ = 8 \times \frac{ {x}^{8} }{8} - \frac{3}{2} \times 2 \sqrt{x} + C = {x}^{8} - 3 \sqrt{x} + C[/tex]
Объяснение:
[tex] \int \frac{1}{ \sqrt{x} } dx = \int {x}^{ - \frac{1}{2} } dx = \frac{ {x}^{ - \frac{1}{2} + 1} }{ - \frac{1}{2} + 1 } + C= \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} } + C= 2 \sqrt{x} +C \\ [/tex]
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Ответ:
[tex]f(x) = 8 {x}^{7} - \frac{3}{2 \sqrt{x} } \\ F(x) = \int \: f(x) dx = \int(8 {x}^{7} - \frac{3}{2 \sqrt{x} } )dx = \\ = 8 \times \frac{ {x}^{8} }{8} - \frac{3}{2} \times 2 \sqrt{x} + C = {x}^{8} - 3 \sqrt{x} + C[/tex]
Объяснение:
[tex] \int \frac{1}{ \sqrt{x} } dx = \int {x}^{ - \frac{1}{2} } dx = \frac{ {x}^{ - \frac{1}{2} + 1} }{ - \frac{1}{2} + 1 } + C= \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} } + C= 2 \sqrt{x} +C \\ [/tex]