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

\int \frac{1}{2 x - 2} d x

\int 2 cos^{2} (4 x) sin (4 x) d x

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{\frac{1}{2}})

x \to \infty lim (sec (x))

f (x) = 5 x, at x = 4, x = 9