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

The integral of ((2x+3))/(sqrt(x)) is 2sqrt(x)(2x+3)-8/3 x^{3/2}+C

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

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

2 x (2 x + 3) - \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

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

Apply Integration By Parts

: 2 x (2 x + 3) - \int 4 x d x

= 2 x (2 x + 3) - \int 4 x d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= 2 x (2 x + 3) - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 2 x (2 x + 3) - \frac{8}{3} x^{\frac{3}{2}} + C

y^{^{''}} + 2 y^{^{'}} + 2 y = 8 e^{2 t}, y (0) = 0, y^{^{'}} (0) = 1

\frac{d y}{d t} = 0.5 y, y (2) = 100

\int \frac{x ^{2}}{x ^{3} - 5 x} d x

\int 3^{c s c (x)} csc (x) cot (x) d x

9 sin (2 x)

What is the integral of ((2x+3))/(sqrt(x)) ?
The integral of ((2x+3))/(sqrt(x)) is 2sqrt(x)(2x+3)-8/3 x^{3/2}+C