integral of 3/4+4/5 x^2-5/6 x^3

解答

\int \frac{3}{4} + \frac{4}{5} x^{2} - \frac{5}{6} x^{3} d x

\frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24} + C

求解步骤

\int \frac{3}{4} + \frac{4}{5} x^{2} - \frac{5}{6} x^{3} 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 \frac{3}{4} d x + \int \frac{4}{5} x^{2} d x - \int \frac{5}{6} x^{3} d x

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

\int \frac{4}{5} x^{2} d x = \frac{4 x ^{3}}{15}

\int \frac{5}{6} x^{3} d x = \frac{5 x ^{4}}{24}

= \frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24}

解答补常数

= \frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24} + C

d er i v a t i v e 5 x + 7 x

x \to 2 lim (3 \frac{x ^{3} - 8}{x - 2})

t a y l or 1 + x

\frac{d}{d x} (\frac{e ^{x} + 1}{e ^{x} + 2})

x \to 2 lim (\frac{x ^{3} - 8}{x - 2})