What is the integral of (2-x)^4 ?

The integral of (2-x)^4 is -((2-x)^5)/5+C

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integral of (2-x)^4

\int (2 - x)^{4} d x

- \frac{( 2 - x ) ^{5}}{5} + C

Solution steps

\int (2 - x)^{4} d x

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

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

= - \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - \frac{u ^{5}}{5}

Substitute back

u = 2 - x

= - \frac{( 2 - x ) ^{5}}{5}

Add a constant to the solution

= - \frac{( 2 - x ) ^{5}}{5} + C

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