What is antiderivative in y=ln3x?(explain please)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that the antiderivative is the opposite of derivative and you need to integrate the given function to find the original function.

You need to use the formula of integration by parts such that:

`int udv = uv - int vdu`

`int ln(3x)dx = int (x')*ln(3x)dx`

`` `u = ln (3x) =gt du = 3/(3x) = 1/x`

`dv = dx =gt v = x`

`` `int ln(3x)dx = x*ln (3x) - int x*(1/x)*dx`

`int ln(3x)dx = x*ln (3x) - x + c=gt int ln(3x)dx = x*(ln (3x) - 1)+c`

Hence, evaluating the antiderivative of the function yields: `int ln(3x)dx = x*(ln (3x) - 1) + c.`