What is the integral of ln(x^3) ?

The integral of ln(x^3) is 3xln(x)-3x+C

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integral of ln(x^3)

\int ln (x^{3}) d x

3 x ln (x) - 3 x + C

Solution steps

\int ln (x^{3}) d x

Apply Integration By Parts

: x ln (x^{3}) - \int 3 d x

= x ln (x^{3}) - \int 3 d x

\int 3 d x = 3 x

= x ln (x^{3}) - 3 x

Apply log rule

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

assuming

x \geq 0

= 3 x ln (x) - 3 x

Add a constant to the solution

= 3 x ln (x) - 3 x + C

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