What is the integral of 21x^2ln(x) ?

The integral of 21x^2ln(x) is 21(1/3 x^3ln(x)-(x^3)/9)+C

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integral of 21x^2ln(x)

\int 21 x^{2} ln (x) d x

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

Solution steps

\int 21 x^{2} ln (x) d x

Take the constant out:

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

= 21 \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

= 21 (\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}

= 21 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= 21 (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

\frac{d y}{d t} = t e^{2 y}

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

\frac{1}{x} d x + d y = 0

arctan (e^{4 x})

What is the integral of 21x^2ln(x) ?
The integral of 21x^2ln(x) is 21(1/3 x^3ln(x)-(x^3)/9)+C