What is the integral of 9(ln(x))^2 ?

The integral of 9(ln(x))^2 is 9(xln^2(x)-2(xln(x)-x))+C

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integral of 9(ln(x))^2

\int 9 (ln (x))^{2} d x

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

Solution steps

\int 9 (ln (x))^{2} d x

Take the constant out:

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

= 9 \cdot \int (ln (x))^{2} d x

Apply Integration By Parts

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

= 9 (x ln^{2} (x) - \int 2 ln (x) d x)

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

= 9 (x ln^{2} (x) - 2 (x ln (x) - x))

Add a constant to the solution

= 9 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

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

\frac{\partial}{\partial x} (cos (2 x) sin (3 y))

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 1

\frac{d ^{2} y}{d x ^{2}} = 4 x cos (x^{2})

3 y^{^{'}} + y = (1 - 2 x) y^{4}

What is the integral of 9(ln(x))^2 ?
The integral of 9(ln(x))^2 is 9(xln^2(x)-2(xln(x)-x))+C