What is the integral of (3ln^2(x))/(x^2) ?

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

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integral of (3ln^2(x))/(x^2)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \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

= 3 (- \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})

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x sec ( - ( \frac{y}{x} ) + y )}{x})

\int (x^{2} - 1)^{3} d x

\int sin (t^{4}) d t

f (t) = 1 + t

\frac{d}{d x} (y (x))

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