integral of (x^2+2x+1)

解答

\int (x^{2} + 2 x + 1) d x

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

求解步骤

\int x^{2} + 2 x + 1 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 x^{2} d x + \int 2 x d x + \int 1 d x

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

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

\int 1 d x = x

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

解答补常数

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

d er i v a t i v e f (x) = (- 25 x^{2} + 1)^{2}

\int \frac{1}{3} cos (3 x) d x

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0, y (0) = 0

\frac{\partial}{\partial c} (c^{\frac{1}{2}} + l^{\frac{1}{2}})

\frac{d}{d x} (\frac{x ^{3}}{3} - x^{2} + 2)