What is the integral of 5x^2ln(x) ?

The integral of 5x^2ln(x) is 5(1/3 x^3ln(x)-(x^3)/9)+C

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integral of 5x^2ln(x)

\int 5 x^{2} ln (x) d x

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

Solution steps

\int 5 x^{2} ln (x) d x

Take the constant out:

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

= 5 \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

= 5 (\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}

= 5 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= 5 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

x = 6 y - y^{2}, x = 0

\frac{d y}{d x} = e^{5 x + 2 y}

\frac{2}{s ^{2} + 2}

\frac{d}{d x} (x (x^{4} + 5)^{5})

\int_{0}^{\infty} a e^{- a x} d x

What is the integral of 5x^2ln(x) ?
The integral of 5x^2ln(x) is 5(1/3 x^3ln(x)-(x^3)/9)+C