What is the integral of 7sqrt(16-2x) ?

The integral of 7sqrt(16-2x) is -7/3 (16-2x)^{3/2}+C

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integral of 7sqrt(16-2x)

\int 7 16 - 2 x d x

- \frac{7}{3} (16 - 2 x)^{\frac{3}{2}} + C

Solution steps

\int 7 16 - 2 x d x

Take the constant out:

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

= 7 \cdot \int 16 - 2 x d x

Apply u-substitution

: \int - \frac{u}{2} d u

= 7 \cdot \int - \frac{u}{2} d u

Take the constant out:

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

= 7 (- \frac{1}{2} \cdot \int u d u)

Apply the Power Rule

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

= 7 (- \frac{1}{2} \cdot \frac{2}{3} u^{\frac{3}{2}})

Substitute back

u = 16 - 2 x

= 7 (- \frac{1}{2} \cdot \frac{2}{3} (16 - 2 x)^{\frac{3}{2}})

Simplify

7 (- \frac{1}{2} \cdot \frac{2}{3} (16 - 2 x)^{\frac{3}{2}}) : - \frac{7}{3} (16 - 2 x)^{\frac{3}{2}}

= - \frac{7}{3} (16 - 2 x)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{7}{3} (16 - 2 x)^{\frac{3}{2}} + C

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What is the integral of 7sqrt(16-2x) ?
The integral of 7sqrt(16-2x) is -7/3 (16-2x)^{3/2}+C