integral of (3x-5)^2

解答

\int (3 x - 5)^{2} d x

3 x^{3} - 15 x^{2} + 25 x + C

求解步骤

\int (3 x - 5)^{2} d x

乘开

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

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

\int 9 x^{2} d x = 3 x^{3}

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

\int 25 d x = 25 x

= 3 x^{3} - 15 x^{2} + 25 x

解答补常数

= 3 x^{3} - 15 x^{2} + 25 x + C

n = 1 \sum \infty \frac{1}{n ^{1.1}}

\int \frac{7}{6 + 7 x} d x

x \to 9 lim (\frac{x + 9}{x - 9})

\frac{d}{d x} (sin (ln (1 - 3 x)))

\frac{d}{d t} (\frac{d x}{d t}) + x = sin (2 t)