integral of ((x+5)(x-2))/(sqrt(x))

解答

\int \frac{( x + 5 ) ( x - 2 )}{x} d x

\frac{2}{5} x^{2} x + 2 x x - 20 x + C

求解步骤

\int \frac{( x + 5 ) ( x - 2 )}{x} d x

使用分布积分法

= x (x + 5) (x - 2) - \int \frac{3 x ^{2} + 3 x + 10}{2 x} d x

\int \frac{3 x ^{2} + 3 x + 10}{2 x} d x = \frac{1}{5} x (3 x^{2} + 5 x + 50)

= x (x + 5) (x - 2) - \frac{1}{5} x (3 x^{2} + 5 x + 50)

化简

x (x + 5) (x - 2) - \frac{1}{5} x (3 x^{2} + 5 x + 50) : \frac{2}{5} x^{2} x + 2 x x - 20 x

= \frac{2}{5} x^{2} x + 2 x x - 20 x

解答补常数

= \frac{2}{5} x^{2} x + 2 x x - 20 x + C

\int 5 x e^{x} d x

\int \frac{x + 2}{( x - 5 ) ( x + 3 )} d x

\int \frac{1}{3 ^{2} + x ^{2}} d x

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

\int \frac{3}{[ x ( x + 3 ) ]} d x