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

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

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integral of (1+3sqrt(x))

\int (1 + 3 x) d x

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

Solution steps

\int 1 + 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 1 d x + \int 3 x d x

\int 1 d x = x

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

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

Add a constant to the solution

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

\frac{\partial}{\partial z} (x - y)

\int \frac{x + 3}{4 x + 4} d x

cos (\frac{2}{3} x)

\int sin (x) cos^{7} (x) d x

\frac{d}{d x} (24 x)

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