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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

n \to 1 lim (3 - \frac{7}{4 ^{n}})

\frac{\partial}{\partial x} (x y^{10} + x^{2} + y^{4})

\int (e^{3 x} + 1) d x

\int x^{2} cos (y) + 3 y^{2} e^{x} d y

e^{x^{8}}

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