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

The integral of (2/(sqrt(x))-3xsqrt(x)+2) is 4sqrt(x)-6/5 x^{5/2}+2x+C

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

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

4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x + C

Solution steps

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

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

\int 3 x x d x = \frac{6}{5} x^{\frac{5}{2}}

\int 2 d x = 2 x

= 4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x

Add a constant to the solution

= 4 x - \frac{6}{5} x^{\frac{5}{2}} + 2 x + C

What is the integral of (2/(sqrt(x))-3xsqrt(x)+2) ?
The integral of (2/(sqrt(x))-3xsqrt(x)+2) is 4sqrt(x)-6/5 x^{5/2}+2x+C