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

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

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integral of 3(ln(x))^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 2 ln (x) d x = 2 (x ln (x) - x)

= 3 (x ln^{2} (x) - 2 (x ln (x) - x))

Add a constant to the solution

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

\int x (x - 3) d x

\frac{d}{d x} ((cos (x^{3}))^{2})

2 x y + x^{3} = \frac{x d y}{d x}

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t

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

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