What is the integral of ln(7x^5) ?

The integral of ln(7x^5) is x(ln(7)+5ln(x))-5x+C

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integral of ln(7x^5)

\int ln (7 x^{5}) d x

x (ln (7) + 5 ln (x)) - 5 x + C

Solution steps

\int ln (7 x^{5}) d x

Apply Integration By Parts

= x ln (7 x^{5}) - \int 5 d x

\int 5 d x = 5 x

= x ln (7 x^{5}) - 5 x

Simplify

ln (7 x^{5}) : 5 ln (x) + ln (7)

= x (ln (7) + 5 ln (x)) - 5 x

Add a constant to the solution

= x (ln (7) + 5 ln (x)) - 5 x + C

\frac{\partial}{\partial x} (e^{x} sin (y))

\frac{d y}{d x} - 9 y^{2} e^{- 3 x} = 0, y (0) = 10

\int (\frac{3}{2 x ^{\frac{1}{2}}} - \frac{2}{3 x ^{\frac{1}{3}}}) d x

\frac{d}{d x} (\frac{2}{3} x^{\frac{3}{2}} + 1)

\frac{d}{d x} (x^{3} - 3 x^{2} - 24 x + 32)

What is the integral of ln(7x^5) ?
The integral of ln(7x^5) is x(ln(7)+5ln(x))-5x+C