What is the integral of (2x-7)^{73} ?

The integral of (2x-7)^{73} is 1/148 (2x-7)^{74}+C

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integral of (2x-7)^{73}

\int (2 x - 7)^{73} d x

\frac{1}{148} (2 x - 7)^{74} + C

Solution steps

\int (2 x - 7)^{73} d x

Apply u-substitution

: \int \frac{u ^{73}}{2} d u

= \int \frac{u ^{73}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{73} d u

Apply the Power Rule

: \frac{u ^{74}}{74}

= \frac{1}{2} \cdot \frac{u ^{74}}{74}

Substitute back

u = 2 x - 7

= \frac{1}{2} \cdot \frac{( 2 x - 7 ) ^{74}}{74}

Simplify

\frac{1}{2} \cdot \frac{( 2 x - 7 ) ^{74}}{74} : \frac{1}{148} (2 x - 7)^{74}

= \frac{1}{148} (2 x - 7)^{74}

Add a constant to the solution

= \frac{1}{148} (2 x - 7)^{74} + C

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What is the integral of (2x-7)^{73} ?
The integral of (2x-7)^{73} is 1/148 (2x-7)^{74}+C