What is the integral of 85-3sqrt(25-x) ?

The integral of 85-3sqrt(25-x) is 85x+2(25-x)^{3/2}+C

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integral of 85-3sqrt(25-x)

\int 85 - 3 25 - x d x

85 x + 2 (25 - x)^{\frac{3}{2}} + C

Solution steps

\int 85 - 3 25 - 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 85 d x - \int 3 25 - x d x

\int 85 d x = 85 x

\int 3 25 - x d x = - 2 (25 - x)^{\frac{3}{2}}

= 85 x - (- 2 (25 - x)^{\frac{3}{2}})

Simplify

= 85 x + 2 (25 - x)^{\frac{3}{2}}

Add a constant to the solution

= 85 x + 2 (25 - x)^{\frac{3}{2}} + C

What is the integral of 85-3sqrt(25-x) ?
The integral of 85-3sqrt(25-x) is 85x+2(25-x)^{3/2}+C