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

The integral of ((3+sqrt(x))^2)/x is x+12sqrt(x)+9ln|x|+9+C

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

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

x + 12 x + 9 ln ∣ x ∣ + 9 + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{- 3 x - 9}{x} d x = - 6 x - 9 ln ∣ x ∣

= (3 + x)^{2} - (- 6 x - 9 ln ∣ x ∣)

Simplify

(3 + x)^{2} - (- 6 x - 9 ln ∣ x ∣) : x + 12 x + 9 ln ∣ x ∣ + 9

= x + 12 x + 9 ln ∣ x ∣ + 9

Add a constant to the solution

= x + 12 x + 9 ln ∣ x ∣ + 9 + C

\int 3 x 2 x + 3 d x

\int cos^{3} (\frac{x}{8}) d x

y = \frac{1}{x ^{5}}, (3, \frac{1}{243})

\int_{- 3}^{3} 18 - 2 x^{2} d x

x \to 2 - lim (\frac{3 - x}{2 - x})

What is the integral of ((3+sqrt(x))^2)/x ?
The integral of ((3+sqrt(x))^2)/x is x+12sqrt(x)+9ln|x|+9+C