integral of 5x^2+9

解答

\int 5 x^{2} + 9 d x

\frac{5 x ^{3}}{3} + 9 x + C

求解步骤

\int 5 x^{2} + 9 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 5 x^{2} d x + \int 9 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 9 d x = 9 x

= \frac{5 x ^{3}}{3} + 9 x

解答补常数

= \frac{5 x ^{3}}{3} + 9 x + C