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

The integral of (2sqrt(x)-3/(sqrt(x))) is 4/3 x^{3/2}-6sqrt(x)+C

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

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

\frac{4}{3} x^{\frac{3}{2}} - 6 x + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x d x - \int \frac{3}{x} d x

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

\int \frac{3}{x} d x = 6 x

= \frac{4}{3} x^{\frac{3}{2}} - 6 x

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - 6 x + C

\int_{1}^{e^{2}} x^{5} ln (x) d x

\int x y e^{x y^{2}} d y

\frac{d}{d x} (\frac{6 x}{x ^{2} - 4})

\int_{0}^{N} e^{- s t} e^{- 4 t} d t

x \to + 0 + lim (\frac{5 x}{sin ( x )})

What is the integral of (2sqrt(x)-3/(sqrt(x))) ?
The integral of (2sqrt(x)-3/(sqrt(x))) is 4/3 x^{3/2}-6sqrt(x)+C