integral of (sqrt(x)+7)(sqrt(x)-7)

解答

\int (x + 7) (x - 7) d x

\frac{x ^{2}}{2} - 49 x + C

求解步骤

\int (x + 7) (x - 7) d x

乘以

x + 7

的共轭根式

: \frac{x - 49}{x - 7}

= \int \frac{x - 49}{x - 7} (x - 7) d x

化简

\frac{x - 49}{x - 7} (x - 7) : x - 49

= \int x - 49 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 d x - \int 49 d x

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

\int 49 d x = 49 x

= \frac{x ^{2}}{2} - 49 x

解答补常数

= \frac{x ^{2}}{2} - 49 x + C

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