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

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

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

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

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

Solution steps

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

Simplify

(ln (x))^{2} \frac{1}{x ^{2}} : \frac{ln ^{2} ( x )}{x ^{2}}

= \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

\frac{\partial}{\partial x} (sin (5 x y + 4 yz + 7 x z))

f (x) = \frac{- 8 x}{x ^{2} + 1}, (0, 0)

\int_{2}^{5} x d x

\int e^{- \frac{1}{2} z^{2}}

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

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