integral of (1+20w)sqrt(w)

解答

\int (1 + 20 w) w d w

\frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}} + C

求解步骤

\int (1 + 20 w) w d w

使用分布积分法

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \int \frac{40}{3} w^{\frac{3}{2}} d w

\int \frac{40}{3} w^{\frac{3}{2}} d w = \frac{16}{3} w^{\frac{5}{2}}

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}}

解答补常数

= \frac{2}{3} w^{\frac{3}{2}} (1 + 20 w) - \frac{16}{3} w^{\frac{5}{2}} + C

\int \frac{x ^{2}}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (e^{3 x} \cdot 3)

\int cos (6 y) - cos (- 6 y) d y

\frac{d}{d x} (\frac{1}{3 x + 6})

d er i v a t i v e (\frac{1}{1 - 2 x})^{3}