What is the integral of 2/(1-x)+((ln(x))^2)/x ?

The integral of 2/(1-x)+((ln(x))^2)/x is -2ln|1-x|+(ln^3(x))/3+C

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integral of 2/(1-x)+((ln(x))^2)/x

\int \frac{2}{1 - x} + \frac{( ln ( x ) ) ^{2}}{x} d x

- 2 ln ∣ 1 - x ∣ + \frac{ln ^{3} ( x )}{3} + C

Solution steps

\int \frac{2}{1 - x} + \frac{( ln ( x ) ) ^{2}}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{1 - x} d x + \int \frac{( ln ( x ) ) ^{2}}{x} d x

\int \frac{2}{1 - x} d x = - 2 ln ∣ 1 - x ∣

\int \frac{( ln ( x ) ) ^{2}}{x} d x = \frac{ln ^{3} ( x )}{3}

= - 2 ln ∣ 1 - x ∣ + \frac{ln ^{3} ( x )}{3}

Add a constant to the solution

= - 2 ln ∣ 1 - x ∣ + \frac{ln ^{3} ( x )}{3} + C

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What is the integral of 2/(1-x)+((ln(x))^2)/x ?
The integral of 2/(1-x)+((ln(x))^2)/x is -2ln|1-x|+(ln^3(x))/3+C