Use the reduction formula: ∫ (ln x)^n dx = x(ln x)^n - n ∫ (ln x)^n-1 dx to evaluate ∫ (ln x)^3

Step 1: Start with the given integral ∫ln(x)dx.

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Use the reduction formula: $\int (\ln x)^n dx = x(\ln x)^n - n \int (\ln x)^{n-1} dx$ to evaluate $\int (\ln x)^3 dx$. To achieve this, you will need to apply the reduction formula 3 times. First application of the reduction formula ($n = 3$): $\int (\ln x)^3 dx = \square + \int \square dx$. Second application of the reduction formula ($n = 2$): $\int (\ln x)^3 dx = \square + \int \square dx$. Third application of the reduction formula: ($n = 1$) $\int (\ln x)^3 dx = \square + \int \square dx$. Wrap-up: So completing the final integration above, $\int (\ln x)^3 dx = \square + C$.

          Use the reduction formula: $\int (\ln x)^n dx = x(\ln x)^n - n \int (\ln x)^{n-1} dx$ to evaluate $\int (\ln x)^3 dx$.
To achieve this, you will need to apply the reduction formula 3 times.
First application of the reduction formula ($n = 3$):
$\int (\ln x)^3 dx = \square + \int \square dx$.
Second application of the reduction formula ($n = 2$):
$\int (\ln x)^3 dx = \square + \int \square dx$.
Third application of the reduction formula: ($n = 1$)
$\int (\ln x)^3 dx = \square + \int \square dx$.
Wrap-up: So completing the final integration above,
$\int (\ln x)^3 dx = \square + C$.

Use the reduction formula: ∫ (ln x)^n dx = x(ln x)^n - n ∫ (ln x)^n-1 dx to evaluate ∫ (ln x)^3 dx.
To achieve this, you will need to apply the reduction formula 3 times.
First application of the reduction formula (n = 3):
∫ (ln x)^3 dx = □ + ∫□ dx.
Second application of the reduction formula (n = 2):
∫ (ln x)^3 dx = □ + ∫□ dx.
Third application of the reduction formula: (n = 1)
∫ (ln x)^3 dx = □ + ∫□ dx.
Wrap-up: So completing the final integration above,
∫ (ln x)^3 dx = □ + C.

Added by Michelle S.

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