What is the integral of 3sqrt(x)+1/(sqrt(x)) ?

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

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integral of 3sqrt(x)+1/(sqrt(x))

\int 3 x + \frac{1}{x} d x

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

Solution steps

\int 3 x + \frac{1}{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{1}{x} d x

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

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

= 2 x^{\frac{3}{2}} + 2 x

Add a constant to the solution

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

\frac{df}{d s} = 12 s + \frac{5 s}{9 - s ^{2}}

x \to 0 lim (x^{n})

y = x^{3} cos (x)

\int_{0}^{2} (\frac{x + 2}{x - 4}) d x

\int e^{7 θ} sin (8 θ) d θ

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