What is the integral of 3x^2ln(x) ?

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

Popular >

integral of 3x^2ln(x)

\int 3 x^{2} ln (x) d x

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

Solution steps

\int 3 x^{2} ln (x) d x

Take the constant out:

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

= 3 \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

= 3 (\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}

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

Simplify

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

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

Add a constant to the solution

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

x \to 0 lim (- 2 g (x))

\frac{\partial}{\partial x} (x^{2} + x)

\int 7 cot^{3} (x) csc^{3} (x) d x

f (y) = e^{3 y}

n = 0 \sum \infty 1 (n + 1)

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