What is the integral of-6xln^2(x) ?

The integral of-6xln^2(x) is -6(1/2 x^2ln^2(x)-1/2 x^2ln(x)+(x^2)/4)+C

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integral of-6xln^2(x)

\int - 6 x ln^{2} (x) d x

- 6 (\frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4}) + C

Solution steps

\int - 6 x ln^{2} (x) d x

Take the constant out:

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

= - 6 \cdot \int x ln^{2} (x) d x

Apply Integration By Parts

= - 6 (\frac{1}{2} x^{2} ln^{2} (x) - \int x ln (x) d x)

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}

= - 6 (\frac{1}{2} x^{2} ln^{2} (x) - (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}))

Simplify

= - 6 (\frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4})

Add a constant to the solution

= - 6 (\frac{1}{2} x^{2} ln^{2} (x) - \frac{1}{2} x^{2} ln (x) + \frac{x ^{2}}{4}) + C

What is the integral of-6xln^2(x) ?
The integral of-6xln^2(x) is -6(1/2 x^2ln^2(x)-1/2 x^2ln(x)+(x^2)/4)+C