integral of (1+30w)sqrt(w)

解答

\int (1 + 30 w) w d w

\frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}} + C

求解步骤

\int (1 + 30 w) w d w

使用分布积分法

= \frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - \int 20 w^{\frac{3}{2}} d w

\int 20 w^{\frac{3}{2}} d w = 8 w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - 8 w^{\frac{5}{2}}

化简

\frac{2}{3} w^{\frac{3}{2}} (1 + 30 w) - 8 w^{\frac{5}{2}} : \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}}

解答补常数

= \frac{2}{3} w^{\frac{3}{2}} + 12 w^{\frac{5}{2}} + C

d er i v a t i v e f (x) = 6 x + 8

d er i v a t i v e e^{3 - x}

d er i v a t i v e f (x) = 2^{4 x} + 4 x^{2}

y^{^{'}} + x y = x y^{3}

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