What is the integral of (2sqrt(x)-6) ?

The integral of (2sqrt(x)-6) is 4/3 x^{3/2}-6x+C

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integral of (2sqrt(x)-6)

\int (2 x - 6) d x

\frac{4}{3} x^{\frac{3}{2}} - 6 x + C

Solution steps

\int 2 x - 6 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 2 x d x - \int 6 d x

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

\int 6 d x = 6 x

= \frac{4}{3} x^{\frac{3}{2}} - 6 x

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - 6 x + C

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What is the integral of (2sqrt(x)-6) ?
The integral of (2sqrt(x)-6) is 4/3 x^{3/2}-6x+C