What is the integral of yln(y)-1/(sqrt(9-y^2)) ?

The integral of yln(y)-1/(sqrt(9-y^2)) is 1/2 y^2ln(y)-(y^2)/4-arcsin(1/3 y)+C

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integral of yln(y)-1/(sqrt(9-y^2))

\int y ln (y) - \frac{1}{9 - y ^{2}} d y

\frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4} - arcsin (\frac{1}{3} y) + C

Solution steps

\int y ln (y) - \frac{1}{9 - y ^{2}} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int y ln (y) d y = \frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4}

\int \frac{1}{9 - y ^{2}} d y = arcsin (\frac{1}{3} y)

= \frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4} - arcsin (\frac{1}{3} y)

Add a constant to the solution

= \frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4} - arcsin (\frac{1}{3} y) + C

\frac{\partial}{\partial x} (2 x - 10)

\int k t d t

\int x^{3} z e^{x z} d x

n = 0 \sum \infty - 6 (- \frac{1}{3})^{2 n}

f (x) = 2 x^{3} ln (x)

What is the integral of yln(y)-1/(sqrt(9-y^2)) ?
The integral of yln(y)-1/(sqrt(9-y^2)) is 1/2 y^2ln(y)-(y^2)/4-arcsin(1/3 y)+C