What is the integral of 4ln(4x^2) ?

The integral of 4ln(4x^2) is 4(2xln(2x)-2x)+C

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integral of 4ln(4x^2)

\int 4 ln (4 x^{2}) d x

4 (2 x ln (2 x) - 2 x) + C

Solution steps

\int 4 ln (4 x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int ln (4 x^{2}) d x

Apply Integration By Parts

: x ln (4 x^{2}) - \int 2 d x

= 4 (x ln (4 x^{2}) - \int 2 d x)

\int 2 d x = 2 x

= 4 (x ln (4 x^{2}) - 2 x)

Simplify

ln (4 x^{2}) : 2 ln (2 x)

= 4 (2 x ln (2 x) - 2 x)

Add a constant to the solution

= 4 (2 x ln (2 x) - 2 x) + C

\frac{d}{d x} (\frac{a ^{2} + x ^{2}}{a ^{2} - x ^{2}})

\int u^{3} d u

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

\frac{2 x - 1}{4 x + 8}

What is the integral of 4ln(4x^2) ?
The integral of 4ln(4x^2) is 4(2xln(2x)-2x)+C