What is the integral of (7-x)^{49} ?

The integral of (7-x)^{49} is -((7-x)^{50})/(50)+C

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integral of (7-x)^{49}

\int (7 - x)^{49} d x

- \frac{( 7 - x ) ^{50}}{50} + C

Solution steps

\int (7 - x)^{49} d x

Apply u-substitution

= \int - u^{49} d u

Take the constant out:

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

= - \int u^{49} d u

Apply the Power Rule

= - \frac{u ^{50}}{50}

Substitute back

u = 7 - x

= - \frac{( 7 - x ) ^{50}}{50}

Add a constant to the solution

= - \frac{( 7 - x ) ^{50}}{50} + C

What is the integral of (7-x)^{49} ?
The integral of (7-x)^{49} is -((7-x)^{50})/(50)+C