integral of (-6x^2y+7xy)

解答

\int (- 6 x^{2} y + 7 x y) d y

- 3 x^{2} y^{2} + \frac{7 x y ^{2}}{2} + C

求解步骤

\int - 6 x^{2} y + 7 x 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 6 x^{2} y d y + \int 7 x y d y

\int 6 x^{2} y d y = 3 x^{2} y^{2}

\int 7 x y d y = \frac{7 x y ^{2}}{2}

= - 3 x^{2} y^{2} + \frac{7 x y ^{2}}{2}

解答补常数

= - 3 x^{2} y^{2} + \frac{7 x y ^{2}}{2} + C

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