What is the integral of ye^{y^2}-y ?

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

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integral of ye^{y^2}-y

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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