integral of (2x^2+3x+7)

解答

\int (2 x^{2} + 3 x + 7) d x

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

求解步骤

\int 2 x^{2} + 3 x + 7 d x

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 2 x^{2} d x + \int 3 x d x + \int 7 d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 7 d x = 7 x

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

解答补常数

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

d er i v a t i v e f (x) = 7 x^{3} e^{- x}

\int e^{2 x} sin (e^{2 x}) d x

d er i v a t i v e y = 10000 + 30 x e^{\frac{x}{800}}

a re a x + 2 y = 2, y - x = 1, 2 x + y = 7

\frac{d}{d x} (\frac{π}{x})