What is the integral of ln((5x)^2) ?

The integral of ln((5x)^2) is 2xln(5x)-2x+C

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integral of ln((5x)^2)

\int ln ((5 x)^{2}) d x

2 x ln (5 x) - 2 x + C

Solution steps

\int ln ((5 x)^{2}) d x

Apply Integration By Parts

= x ln (25 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (25 x^{2}) - 2 x

Simplify

ln (25 x^{2}) : 2 ln (5 x)

= 2 x ln (5 x) - 2 x

Add a constant to the solution

= 2 x ln (5 x) - 2 x + C

What is the integral of ln((5x)^2) ?
The integral of ln((5x)^2) is 2xln(5x)-2x+C