What is the integral of e^x-1/2 y^2 ?

The integral of e^x-1/2 y^2 is e^x-1/2 y^2x+C

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integral of e^x-1/2 y^2

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

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

Solution steps

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

Apply the Sum Rule:

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

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

\int e^{x} d x = e^{x}

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

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

Add a constant to the solution

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

- 2 x^{\frac{3}{2}}

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

y = 9 x^{3}

\frac{\partial}{\partial x} (2 y + x^{2} cos (t))

y^{^{'}} = \frac{x - 4}{y - 6}

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