What is the indefinite integral of y=(1/x)*(7+lnx)^2 ?

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We need to find the definite integral of y = (1/x)*(7+ln x)^2.

Let u = 7 + ln x

du/dx = 1/x

=> dx / x = du

Int [ y dx] = Int [ (1/x)*(7+ln x)^2 dx ]

=> Int [ u^2 du]

=> u^3 / 3

replace u...

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We need to find the definite integral of y = (1/x)*(7+ln x)^2.

Let u = 7 + ln x

du/dx = 1/x

=> dx / x = du

Int [ y dx] = Int [ (1/x)*(7+ln x)^2 dx ]

=> Int [ u^2 du]

=> u^3 / 3

replace u with 7 + ln x

=> (7 + ln x)^3 / 3

Therefore the integral of y = (1/x)*(7 + ln x)^2 is

(7 + ln x)^3 / 3 + C

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