integral of (5s+3)^2

解答

\int (5 s + 3)^{2} d s

\frac{25 s ^{3}}{3} + 15 s^{2} + 9 s + C

求解步骤

\int (5 s + 3)^{2} d s

乘开

(5 s + 3)^{2} : 25 s^{2} + 30 s + 9

= \int 25 s^{2} + 30 s + 9 d s

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 25 s^{2} d s + \int 30 s d s + \int 9 d s

\int 25 s^{2} d s = \frac{25 s ^{3}}{3}

\int 30 s d s = 15 s^{2}

\int 9 d s = 9 s

= \frac{25 s ^{3}}{3} + 15 s^{2} + 9 s

解答补常数

= \frac{25 s ^{3}}{3} + 15 s^{2} + 9 s + C

n = 0 \sum \infty \frac{7 ^{n}}{1 1 ^{n}}

\int_{0}^{1} \frac{1}{x ^{3}} d x

d er i v a t i v e e^{2} + 2^{x}

x \to 0 + lim (x^{15 x})

n = 5 \sum \infty (\frac{4}{5})^{- n}