What is the integral of (ye^{x^2+y^2}+3y^2) ?

The integral of (ye^{x^2+y^2}+3y^2) is y^3+1/2 e^{x^2+y^2}+C

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integral of (ye^{x^2+y^2}+3y^2)

\int (y e^{x^{2} + y^{2}} + 3 y^{2}) d y

y^{3} + \frac{1}{2} e^{x^{2} + y^{2}} + C

Solution steps

\int y e^{x^{2} + y^{2}} + 3 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 3 y^{2} d y + \int e^{x^{2} + y^{2}} y d y

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

\int e^{x^{2} + y^{2}} y d y = \frac{1}{2} e^{x^{2} + y^{2}}

= y^{3} + \frac{1}{2} e^{x^{2} + y^{2}}

Add a constant to the solution

= y^{3} + \frac{1}{2} e^{x^{2} + y^{2}} + C

\frac{d}{d x} (\frac{x ^{5}}{6} + \frac{1}{10 x ^{3}})

f (x) = \frac{2 - 3 x - x ^{2}}{x ^{2} - 4}

\int \frac{4 x}{x ^{2} - 1} d x

y^{^{''}} + 4 y^{^{'}} = 2 x - 3 e^{x}

\int 5 cos^{3} (x) d x

What is the integral of (ye^{x^2+y^2}+3y^2) ?
The integral of (ye^{x^2+y^2}+3y^2) is y^3+1/2 e^{x^2+y^2}+C