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

The integral of-2x^2ln(x) is -2(1/3 x^3ln(x)-(x^3)/9)+C

Popular >

integral of-2x^2ln(x)

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

- 2 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= - 2 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= - 2 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

\int e^{3 x} sin (e^{- x}) d x

\int (2 x + 4)^{\frac{1}{2}} d x

\int \frac{1}{2 x ^{2} - 7 x + 5} d x

\int \frac{x}{1 - x + 3 x ^{2}} d x

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

What is the integral of-2x^2ln(x) ?
The integral of-2x^2ln(x) is -2(1/3 x^3ln(x)-(x^3)/9)+C