What is the integral of ((x+3)^2)/(sqrt(x)) ?

The integral of ((x+3)^2)/(sqrt(x)) is 2/5 x^2sqrt(x)+4xsqrt(x)+18sqrt(x)+C

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integral of ((x+3)^2)/(sqrt(x))

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

\frac{2}{5} x^{2} x + 4 x x + 18 x + C

Solution steps

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

Apply Integration By Parts

: x (x + 3)^{2} - \int \frac{3 x ^{2} + 6 x - 9}{2 x} d x

= x (x + 3)^{2} - \int \frac{3 x ^{2} + 6 x - 9}{2 x} d x

\int \frac{3 x ^{2} + 6 x - 9}{2 x} d x = \frac{1}{5} x (3 x^{2} + 10 x - 45)

= x (x + 3)^{2} - \frac{1}{5} x (3 x^{2} + 10 x - 45)

Simplify

x (x + 3)^{2} - \frac{1}{5} x (3 x^{2} + 10 x - 45) : \frac{2}{5} x^{2} x + 4 x x + 18 x

= \frac{2}{5} x^{2} x + 4 x x + 18 x

Add a constant to the solution

= \frac{2}{5} x^{2} x + 4 x x + 18 x + C

\int - 1280 (1 + 4 x)^{- 3} d x

\frac{d}{d x} (\frac{x ^{2} - 4}{x})

\int \frac{x ^{4} - 1}{x ^{2} + 1} d x

\int (sec^{2} (x) - 4) d x

x^{- 2}, 4

What is the integral of ((x+3)^2)/(sqrt(x)) ?
The integral of ((x+3)^2)/(sqrt(x)) is 2/5 x^2sqrt(x)+4xsqrt(x)+18sqrt(x)+C