What is the integral of 10sqrt(25-x) ?

The integral of 10sqrt(25-x) is -20/3 (25-x)^{3/2}+C

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integral of 10sqrt(25-x)

\int 10 25 - x d x

- \frac{20}{3} (25 - x)^{\frac{3}{2}} + C

Solution steps

\int 10 25 - x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int 25 - x d x

Apply u-substitution

: \int - u d u

= 10 \cdot \int - u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 (- \int u d u)

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= 10 (- \frac{2}{3} u^{\frac{3}{2}})

Substitute back

u = 25 - x

= 10 (- \frac{2}{3} (25 - x)^{\frac{3}{2}})

Simplify

10 (- \frac{2}{3} (25 - x)^{\frac{3}{2}}) : - \frac{20}{3} (25 - x)^{\frac{3}{2}}

= - \frac{20}{3} (25 - x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{20}{3} (25 - x)^{\frac{3}{2}} + C

x y^{2}

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(\frac{u ^{3} - 1}{u ^{3} + 1})^{8}

\frac{\partial}{\partial x} (4 - 2 xx)

\frac{1}{s ^{2} + 2 s + 1}

What is the integral of 10sqrt(25-x) ?
The integral of 10sqrt(25-x) is -20/3 (25-x)^{3/2}+C