What is the integral from 5 to 7 of x(x-5)^{12} ?

The integral from 5 to 7 of x(x-5)^{12} is

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integral from 5 to 7 of x(x-5)^{12}

\int_{5}^{7} x (x - 5)^{12} d x

\frac{7 ^{14}}{14} - \frac{60 \cdot 7 ^{13}}{13} + \frac{275 \cdot 7 ^{12}}{2} - 2500 \cdot 7^{11} + \frac{61875 \cdot 7 ^{10}}{2} - 275000 \cdot 7^{9} + \frac{3609375 \cdot 7 ^{8}}{2} - \frac{61875000 \cdot 7 ^{7}}{7} + \frac{64453125 \cdot 7 ^{6}}{2} - 85937500 \cdot 7^{5} + \frac{322265625 \cdot 7 ^{4}}{2} - 195312500 \cdot 7^{3} + \frac{244140625 \cdot 7 ^{2}}{2} - (\frac{5 ^{14}}{14} - \frac{60 \cdot 5 ^{13}}{13} + \frac{275 \cdot 5 ^{12}}{2} - 2500 \cdot 5^{11} + \frac{61875 \cdot 5 ^{10}}{2} - 275000 \cdot 5^{9} + \frac{3609375 \cdot 5 ^{8}}{2} - \frac{61875000 \cdot 5 ^{7}}{7} + \frac{64453125 \cdot 5 ^{6}}{2} - 85937500 \cdot 5^{5} + \frac{322265625 \cdot 5 ^{4}}{2} - 195312500 \cdot 5^{3} + \frac{244140625 \cdot 5 ^{2}}{2})

Decimal

4321.05494 \dots

Solution steps

\int_{5}^{7} x (x - 5)^{12} d x

Compute the indefinite integral:

\int x (x - 5)^{12} d x = \frac{x ^{14}}{14} - \frac{60 x ^{13}}{13} + \frac{275 x ^{12}}{2} - 2500 x^{11} + \frac{61875 x ^{10}}{2} - 275000 x^{9} + \frac{3609375 x ^{8}}{2} - \frac{61875000 x ^{7}}{7} + \frac{64453125 x ^{6}}{2} - 85937500 x^{5} + \frac{322265625 x ^{4}}{2} - 195312500 x^{3} + \frac{244140625 x ^{2}}{2} + C

Compute the boundaries:

\int_{5}^{7} x (x - 5)^{12} d x = \frac{7 ^{14}}{14} - \frac{60 \cdot 7 ^{13}}{13} + \frac{275 \cdot 7 ^{12}}{2} - 2500 \cdot 7^{11} + \frac{61875 \cdot 7 ^{10}}{2} - 275000 \cdot 7^{9} + \frac{3609375 \cdot 7 ^{8}}{2} - \frac{61875000 \cdot 7 ^{7}}{7} + \frac{64453125 \cdot 7 ^{6}}{2} - 85937500 \cdot 7^{5} + \frac{322265625 \cdot 7 ^{4}}{2} - 195312500 \cdot 7^{3} + \frac{244140625 \cdot 7 ^{2}}{2} - (\frac{5 ^{14}}{14} - \frac{60 \cdot 5 ^{13}}{13} + \frac{275 \cdot 5 ^{12}}{2} - 2500 \cdot 5^{11} + \frac{61875 \cdot 5 ^{10}}{2} - 275000 \cdot 5^{9} + \frac{3609375 \cdot 5 ^{8}}{2} - \frac{61875000 \cdot 5 ^{7}}{7} + \frac{64453125 \cdot 5 ^{6}}{2} - 85937500 \cdot 5^{5} + \frac{322265625 \cdot 5 ^{4}}{2} - 195312500 \cdot 5^{3} + \frac{244140625 \cdot 5 ^{2}}{2})

= \frac{7 ^{14}}{14} - \frac{60 \cdot 7 ^{13}}{13} + \frac{275 \cdot 7 ^{12}}{2} - 2500 \cdot 7^{11} + \frac{61875 \cdot 7 ^{10}}{2} - 275000 \cdot 7^{9} + \frac{3609375 \cdot 7 ^{8}}{2} - \frac{61875000 \cdot 7 ^{7}}{7} + \frac{64453125 \cdot 7 ^{6}}{2} - 85937500 \cdot 7^{5} + \frac{322265625 \cdot 7 ^{4}}{2} - 195312500 \cdot 7^{3} + \frac{244140625 \cdot 7 ^{2}}{2} - (\frac{5 ^{14}}{14} - \frac{60 \cdot 5 ^{13}}{13} + \frac{275 \cdot 5 ^{12}}{2} - 2500 \cdot 5^{11} + \frac{61875 \cdot 5 ^{10}}{2} - 275000 \cdot 5^{9} + \frac{3609375 \cdot 5 ^{8}}{2} - \frac{61875000 \cdot 5 ^{7}}{7} + \frac{64453125 \cdot 5 ^{6}}{2} - 85937500 \cdot 5^{5} + \frac{322265625 \cdot 5 ^{4}}{2} - 195312500 \cdot 5^{3} + \frac{244140625 \cdot 5 ^{2}}{2})

What is the integral from 5 to 7 of x(x-5)^{12} ?
The integral from 5 to 7 of x(x-5)^{12} is