integral of-x+4-x^2-2x

解答

\int - x + 4 - x^{2} - 2 x d x

- \frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} + 4 x + C

求解步骤

\int - x + 4 - x^{2} - 2 x d x

化简

= \int - x^{2} - 3 x + 4 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 3 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

= - \frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} + 4 x

解答补常数

= - \frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} + 4 x + C

\int sec^{2} (x) (tan (x)) d x

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