What is the integral of (12sqrt(x)+sqrt(2)) ?

The integral of (12sqrt(x)+sqrt(2)) is 8x^{3/2}+sqrt(2)x+C

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integral of (12sqrt(x)+sqrt(2))

\int (12 x + 2) d x

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

Solution steps

\int 12 x + 2 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 12 x d x + \int 2 d x

\int 12 x d x = 8 x^{\frac{3}{2}}

\int 2 d x = 2 x

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

Add a constant to the solution

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

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What is the integral of (12sqrt(x)+sqrt(2)) ?
The integral of (12sqrt(x)+sqrt(2)) is 8x^{3/2}+sqrt(2)x+C