What is the integral of ln(x^9) ?

The integral of ln(x^9) is 9xln(x)-9x+C

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integral of ln(x^9)

\int ln (x^{9}) d x

9 x ln (x) - 9 x + C

Solution steps

\int ln (x^{9}) d x

Apply Integration By Parts

: x ln (x^{9}) - \int 9 d x

= x ln (x^{9}) - \int 9 d x

\int 9 d x = 9 x

= x ln (x^{9}) - 9 x

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 9 x ln (x) - 9 x

Add a constant to the solution

= 9 x ln (x) - 9 x + C

\frac{d}{d x} (\frac{8}{3})

x + 2, \frac{1}{x + 1}, 0, 2

\frac{d y}{d x} = \frac{( 2 x + 2 x y ^{2} )}{( y + 2 x ^{2} y )}

x^{2} + 9

\int \frac{42}{1 - cos ( 6 x )} d x