integral of (4x^5+3x+8)

解答

\int (4 x^{5} + 3 x + 8) d x

\frac{2 x ^{6}}{3} + \frac{3 x ^{2}}{2} + 8 x + C

求解步骤

\int 4 x^{5} + 3 x + 8 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^{5} d x + \int 3 x d x + \int 8 d x

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

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

\int 8 d x = 8 x

= \frac{2 x ^{6}}{3} + \frac{3 x ^{2}}{2} + 8 x

解答补常数

= \frac{2 x ^{6}}{3} + \frac{3 x ^{2}}{2} + 8 x + C

f^{^{'}} (x) = 8 x^{3} - 6 x^{2} + 10 x - 9, f (1) = 24

ma c l a u r in 1 - x^{2}

d er i v a t i v e y = \frac{x}{7 + x}

x \to 1 lim (7 x + 42)

\frac{d}{d x} (5^{m x})