What is the integral of (1+4sqrt(x)) ?

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

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integral of (1+4sqrt(x))

\int (1 + 4 x) d x

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

Solution steps

\int 1 + 4 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 4 x d x

\int 1 d x = x

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

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

Add a constant to the solution

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

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