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

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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

f (x) = (1 + 7 x^{2}) (x - x^{2})

(3, - 5), (8, 4)

\frac{d}{d x} (cos (\frac{1 - e ^{3 x}}{1 + e ^{3 x}}))

y^{^{'}} + 3 y = t + e^{- 2 t}

\int \frac{x ^{2} arcsin ( x )}{1 - x ^{2}} 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