What is the integral of (2-x)^{5/2} ?

The integral of (2-x)^{5/2} is -2/7 (2-x)^{7/2}+C

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integral of (2-x)^{5/2}

\int (2 - x)^{\frac{5}{2}} d x

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

Solution steps

\int (2 - x)^{\frac{5}{2}} d x

Apply u-substitution

= \int - u^{\frac{5}{2}} d u

Take the constant out:

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

= - \int u^{\frac{5}{2}} d u

Apply the Power Rule

= - \frac{2}{7} u^{\frac{7}{2}}

Substitute back

u = 2 - x

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

Add a constant to the solution

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

What is the integral of (2-x)^{5/2} ?
The integral of (2-x)^{5/2} is -2/7 (2-x)^{7/2}+C