What is the integral of y(x^2+y^2) ?

The integral of y(x^2+y^2) is 1/2 y^2(x^2+y^2)-(y^4)/4+C

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integral of y(x^2+y^2)

\int y (x^{2} + y^{2}) d y

\frac{1}{2} y^{2} (x^{2} + y^{2}) - \frac{y ^{4}}{4} + C

Solution steps

\int y (x^{2} + y^{2}) d y

Apply Integration By Parts

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

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

\int y^{3} d y = \frac{y ^{4}}{4}

= \frac{1}{2} y^{2} (x^{2} + y^{2}) - \frac{y ^{4}}{4}

Add a constant to the solution

= \frac{1}{2} y^{2} (x^{2} + y^{2}) - \frac{y ^{4}}{4} + C

\int \frac{sec ^{2} ( x )}{tan ^{7} ( x )} d x

\int csc (x) sec (x) d x

f (x) = 6 x

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

(y - 9)^{2} = y^{^{'}}

What is the integral of y(x^2+y^2) ?
The integral of y(x^2+y^2) is 1/2 y^2(x^2+y^2)-(y^4)/4+C