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

The integral of ln(y^3) is 3yln(y)-3y+C

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integral of ln(y^3)

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

3 y ln (y) - 3 y + C

Solution steps

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

Apply Integration By Parts

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

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

\int 3 d y = 3 y

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

Apply log rule

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

assuming

x \geq 0

= 3 y ln (y) - 3 y

Add a constant to the solution

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

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