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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

y^{^{'}} = y - t, y (0) = 0.5

\int (\frac{4}{x ^{3}}) d x

\frac{d}{d x} (\frac{x ^{2} + 2}{x - 1})

f (x) = (x - 2)^{3} + 10

\int (3 x^{2} + 2) 2 x^{3} + 4 x + 1 d x

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