What is the integral of (5sqrt(x)-3) ?

The integral of (5sqrt(x)-3) is 10/3 x^{3/2}-3x+C

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integral of (5sqrt(x)-3)

\int (5 x - 3) d x

\frac{10}{3} x^{\frac{3}{2}} - 3 x + C

Solution steps

\int 5 x - 3 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 5 x d x - \int 3 d x

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

\int 3 d x = 3 x

= \frac{10}{3} x^{\frac{3}{2}} - 3 x

Add a constant to the solution

= \frac{10}{3} x^{\frac{3}{2}} - 3 x + C

What is the integral of (5sqrt(x)-3) ?
The integral of (5sqrt(x)-3) is 10/3 x^{3/2}-3x+C