integral of (x+5)^2

解答

\int (x + 5)^{2} d x

\frac{x ^{3}}{3} + 5 x^{2} + 25 x + C

求解步骤

\int (x + 5)^{2} d x

乘开

(x + 5)^{2} : x^{2} + 10 x + 25

= \int x^{2} + 10 x + 25 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 10 x d x + \int 25 d x

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

\int 10 x d x = 5 x^{2}

\int 25 d x = 25 x

= \frac{x ^{3}}{3} + 5 x^{2} + 25 x

解答补常数

= \frac{x ^{3}}{3} + 5 x^{2} + 25 x + C

\frac{d}{d x} (arctan (\frac{x}{1 - x ^{2}}))

\frac{d x}{d t} + \frac{1}{t} x = t^{3} x^{4}

\frac{\partial}{\partial x} (\frac{4 x}{3 y})

\int \frac{6 x ^{2} + x + 25}{( x + 1 ) ( x ^{2} + 4 )} d x

d er i v a t i v e \frac{2 w ^{3} - w}{w}