What is the integral from-1 to 5 of x(x-4)^{10} ?

The integral from-1 to 5 of x(x-4)^{10} is -28483068/11

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integral from-1 to 5 of x(x-4)^{10}

\int_{- 1}^{5} x (x - 4)^{10} d x

- \frac{28483068}{11}

Decimal

- 2589369.81818 \dots

Solution steps

\int_{- 1}^{5} x (x - 4)^{10} d x

Apply Integration By Parts

= [\frac{1}{11} x (x - 4)^{11} - \int \frac{1}{11} (x - 4)^{11} d x]_{- 1}^{5}

\int \frac{1}{11} (x - 4)^{11} d x = \frac{1}{132} (x - 4)^{12}

= [\frac{1}{11} x (x - 4)^{11} - \frac{1}{132} (x - 4)^{12}]_{- 1}^{5}

Compute the boundaries:

- \frac{28483068}{11}

= - \frac{28483068}{11}

What is the integral from-1 to 5 of x(x-4)^{10} ?
The integral from-1 to 5 of x(x-4)^{10} is -28483068/11