integral of ye^{y^2}-y

解答

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

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

求解步骤

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

使用积分加法定则:

\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}

解答补常数

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

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