What is the integral of ln(x)*ln(x) ?

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

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integral of ln(x)*ln(x)

\int ln (x) \cdot ln (x) d x

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

Solution steps

\int ln (x) ln (x) d x

Apply Integration By Parts

: ln (x) (x ln (x) - x) - \int ln (x) - 1 d x

= ln (x) (x ln (x) - x) - \int ln (x) - 1 d x

\int ln (x) - 1 d x = x ln (x) - 2 x

= ln (x) (x ln (x) - x) - (x ln (x) - 2 x)

Simplify

ln (x) (x ln (x) - x) - (x ln (x) - 2 x) : x ln^{2} (x) - 2 x ln (x) + 2 x

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

Add a constant to the solution

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

y^{^{''}} x = - 5 sin (8 x)

\frac{\partial}{\partial x} (x ln (z^{7} + x^{5}))

f (x) = (x^{2} + 4 x + 3)^{2}

n = 1 \sum \infty \frac{n}{2 ^{n - 1}}

y^{^{'}} - \frac{1}{x} y = 1

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