What is the integral of ((x+5)(x-2))/(sqrt(x)) ?

The integral of ((x+5)(x-2))/(sqrt(x)) is 2/5 x^2sqrt(x)+2xsqrt(x)-20sqrt(x)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

= 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)

Simplify

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

Add a constant to the solution

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

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What is the integral of ((x+5)(x-2))/(sqrt(x)) ?
The integral of ((x+5)(x-2))/(sqrt(x)) is 2/5 x^2sqrt(x)+2xsqrt(x)-20sqrt(x)+C