What is the integral of (4sqrt(x)-1/(2sqrt(x))) ?

The integral of (4sqrt(x)-1/(2sqrt(x))) is 8/3 x^{3/2}-sqrt(x)+C

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integral of (4sqrt(x)-1/(2sqrt(x)))

\int (4 x - \frac{1}{2 x}) d x

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

Solution steps

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

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

\int \frac{1}{2 x} d x = x

= \frac{8}{3} x^{\frac{3}{2}} - x

Add a constant to the solution

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

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What is the integral of (4sqrt(x)-1/(2sqrt(x))) ?
The integral of (4sqrt(x)-1/(2sqrt(x))) is 8/3 x^{3/2}-sqrt(x)+C