What is the integral of x(x-10)^{10} ?

The integral of x(x-10)^{10} is 1/11 x(x-10)^{11}-1/132 (x-10)^{12}+C

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integral of x(x-10)^{10}

\int x (x - 10)^{10} d x

\frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12} + C

Solution steps

\int x (x - 10)^{10} d x

Apply Integration By Parts

: \frac{1}{11} x (x - 10)^{11} - \int \frac{1}{11} (x - 10)^{11} d x

= \frac{1}{11} x (x - 10)^{11} - \int \frac{1}{11} (x - 10)^{11} d x

\int \frac{1}{11} (x - 10)^{11} d x = \frac{1}{132} (x - 10)^{12}

= \frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12}

Add a constant to the solution

= \frac{1}{11} x (x - 10)^{11} - \frac{1}{132} (x - 10)^{12} + C

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What is the integral of x(x-10)^{10} ?
The integral of x(x-10)^{10} is 1/11 x(x-10)^{11}-1/132 (x-10)^{12}+C