What is the integral of ln((7x)^2) ?

The integral of ln((7x)^2) is 2xln(7x)-2x+C

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integral of ln((7x)^2)

\int ln ((7 x)^{2}) d x

2 x ln (7 x) - 2 x + C

Solution steps

\int ln ((7 x)^{2}) d x

Apply Integration By Parts

: x ln (49 x^{2}) - \int 2 d x

= x ln (49 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (49 x^{2}) - 2 x

Simplify

ln (49 x^{2}) : 2 ln (7 x)

= 2 x ln (7 x) - 2 x

Add a constant to the solution

= 2 x ln (7 x) - 2 x + C

\frac{\partial}{\partial x} (cos (2 x + 4 y))

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

3 \cdot y^{^{'}} = \frac{3 x \cdot y + 18 x ^{2} + 2 y ^{2}}{x ^{2}}, y (1) = 3

f (x) = \frac{- 8 x}{x ^{2} + 1}, at x = 0

What is the integral of ln((7x)^2) ?
The integral of ln((7x)^2) is 2xln(7x)-2x+C