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

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

Popular >

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

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

x + \frac{ln ^{3} ( x )}{3} + C

Solution steps

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

Simplify

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

\int 1 d x = x

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

= x + \frac{ln ^{3} ( x )}{3}

Add a constant to the solution

= x + \frac{ln ^{3} ( x )}{3} + C

\int (9 x^{2} - 5 x + 4) d x

\frac{d}{d x} (sin^{2} (2 x) - cos (2 x))

\frac{\partial}{\partial y} (3 x^{2} y^{2} + \frac{x}{y})

x \to 5 lim (4 x + ∣ x - 5 ∣)

n = 1 \sum \infty \frac{x ^{n}}{1 2 ^{n}}

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