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प्रश्न
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
विकल्प
`1/3 (x + log x)^5` + c
`1/5 (x + log x)^5` + c
`1/12 (x + log x)^5` + c
`1/15 (x + log x)^5` + c
MCQ
रिक्त स्थान भरें
उत्तर
`int ((x + 1)(x + log x))^4/(3x) "dx" = underline(1/15 (x + log x)^5 + "c")`.
Explanation:
Put x + log x = t
`=> (1 + 1/x) "dx" = "dt"`
`=> (x +1)/x "dx" = "dt"`
`therefore int ((x + 1)(x + log x))^4/(3x) "dx" = 1/3 int "t"^4`dt
`= 1/3 * "t"^3/5 + "c"`
`= 1/15 "t"^5 + "c"`
`= 1/15 (x + log x)^5 + "c"`
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