What is the integral of 2y^2ln(y) ?

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

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integral of 2y^2ln(y)

\int 2 y^{2} ln (y) d y

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

Solution steps

\int 2 y^{2} ln (y) d y

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

7 e^{x^{2}}

\int \frac{tan ^{2} ( x )}{sin ( x )} d x

\int x^{2} - 2 y d y

\frac{d y}{d x} = 2 x 1 - y^{2}

d y - (y - 1) 2 d x = 0

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