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

Popular >

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

\int (8 x^{3} - 10 x^{- 6}) d x

\frac{\partial}{\partial x} (e^{x y} ln (y))

\frac{\partial}{\partial x} (x e^{x})

8 x^{3}

x \to 3 lim (\frac{2 x + 3}{x - 2})

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