What is the integral of (7x-3)^{100} ?

The integral of (7x-3)^{100} is -1/707 (-7x+3)^{101}+C

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integral of (7x-3)^{100}

\int (7 x - 3)^{100} d x

- \frac{1}{707} (- 7 x + 3)^{101} + C

Solution steps

\int (7 x - 3)^{100} d x

Factor

7 x - 3 : - (- 7 x + 3)

= \int (- (- 7 x + 3))^{100} d x

Simplify

(- (- 7 x + 3))^{100} : (- 7 x + 3)^{100}

= \int (- 7 x + 3)^{100} d x

Apply u-substitution

: \int - \frac{u ^{100}}{7} d u

= \int - \frac{u ^{100}}{7} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int u^{100} d u

Apply the Power Rule

: \frac{u ^{101}}{101}

= - \frac{1}{7} \cdot \frac{u ^{101}}{101}

Substitute back

u = - 7 x + 3

= - \frac{1}{7} \cdot \frac{( - 7 x + 3 ) ^{101}}{101}

Simplify

- \frac{1}{7} \cdot \frac{( - 7 x + 3 ) ^{101}}{101} : - \frac{1}{707} (- 7 x + 3)^{101}

= - \frac{1}{707} (- 7 x + 3)^{101}

Add a constant to the solution

= - \frac{1}{707} (- 7 x + 3)^{101} + C

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What is the integral of (7x-3)^{100} ?
The integral of (7x-3)^{100} is -1/707 (-7x+3)^{101}+C