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

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

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integral of ln(5x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 2 d x = 2 x

= x ln (5 x^{2}) - 2 x

Simplify

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

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

Add a constant to the solution

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

\int_{1}^{2} 3 4 x^{2} - 3 d x

f (x) = 2 x, 1, 3

\int \frac{cos ( x )}{sin ^{2} ( x ) - 81} d x

x \to 0 + lim (e^{x})

\frac{d}{d x} (ln (cos (e^{x^{2} - s e c (x)})))

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