integral of-4x^2-4x+48

解答

\int - 4 x^{2} - 4 x + 48 d x

- \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x + C

求解步骤

\int - 4 x^{2} - 4 x + 48 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 4 x^{2} d x - \int 4 x d x + \int 48 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 4 x d x = 2 x^{2}

\int 48 d x = 48 x

= - \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x

解答补常数

= - \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x + C

x \to 0 + lim (ln (\frac{7}{x ^{3}}))

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