What is the integral of (9-2x)^{11} ?

The integral of (9-2x)^{11} is x(9-2x)^{11}+1/24 (11(-2x+9)^{12}-108(-2x+9)^{11})+C

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integral of (9-2x)^{11}

\int (9 - 2 x)^{11} d x

x (9 - 2 x)^{11} + \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11}) + C

Solution steps

\int (9 - 2 x)^{11} d x

Apply Integration By Parts

: x (9 - 2 x)^{11} - \int - 22 x (9 - 2 x)^{10} d x

= x (9 - 2 x)^{11} - \int - 22 x (9 - 2 x)^{10} d x

\int - 22 x (9 - 2 x)^{10} d x = - \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11})

= x (9 - 2 x)^{11} - (- \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11}))

Simplify

x (9 - 2 x)^{11} - (- \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11})) : x (9 - 2 x)^{11} + \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11})

= x (9 - 2 x)^{11} + \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11})

Add a constant to the solution

= x (9 - 2 x)^{11} + \frac{1}{24} (11 (- 2 x + 9)^{12} - 108 (- 2 x + 9)^{11}) + C

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What is the integral of (9-2x)^{11} ?
The integral of (9-2x)^{11} is x(9-2x)^{11}+1/24 (11(-2x+9)^{12}-108(-2x+9)^{11})+C