What is the integral of (x/4-3)^{15} ?

The integral of (x/4-3)^{15} is

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integral of (x/4-3)^{15}

\int (\frac{x}{4} - 3)^{15} d x

x (\frac{x}{4} - 3)^{15} - \frac{3}{17179869184} (5 x^{16} - 896 x^{15} + 74880 x^{14} - 3870720 x^{13} + 138378240 x^{12} - 3622993920 x^{11} + 71735279616 x^{10} - 1093109022720 x^{9} + 1.29124 E 13 x^{8} - 1 2^{9} \cdot 22880 x^{7} + 8.2639 E 14 x^{6} - 1 2^{11} \cdot 5824 x^{5} + 1.62273 E 16 x^{4} - 3.99441 E 16 x^{3} + 5.13567 E 16 x^{2}) + C

Solution steps

\int (\frac{x}{4} - 3)^{15} d x

Apply Integration By Parts

: x (\frac{x}{4} - 3)^{15} - \int \frac{15}{1073741824} x (x - 12)^{14} d x

= x (\frac{x}{4} - 3)^{15} - \int \frac{15}{1073741824} x (x - 12)^{14} d x

\int \frac{15}{1073741824} x (x - 12)^{14} d x = \frac{3}{17179869184} (5 x^{16} - 896 x^{15} + 74880 x^{14} - 3870720 x^{13} + 138378240 x^{12} - 3622993920 x^{11} + 71735279616 x^{10} - 1093109022720 x^{9} + 1.29124 E 13 x^{8} - 1 2^{9} \cdot 22880 x^{7} + 8.2639 E 14 x^{6} - 1 2^{11} \cdot 5824 x^{5} + 1.62273 E 16 x^{4} - 3.99441 E 16 x^{3} + 5.13567 E 16 x^{2})

= x (\frac{x}{4} - 3)^{15} - \frac{3}{17179869184} (5 x^{16} - 896 x^{15} + 74880 x^{14} - 3870720 x^{13} + 138378240 x^{12} - 3622993920 x^{11} + 71735279616 x^{10} - 1093109022720 x^{9} + 1.29124 E 13 x^{8} - 1 2^{9} \cdot 22880 x^{7} + 8.2639 E 14 x^{6} - 1 2^{11} \cdot 5824 x^{5} + 1.62273 E 16 x^{4} - 3.99441 E 16 x^{3} + 5.13567 E 16 x^{2})

Add a constant to the solution

= x (\frac{x}{4} - 3)^{15} - \frac{3}{17179869184} (5 x^{16} - 896 x^{15} + 74880 x^{14} - 3870720 x^{13} + 138378240 x^{12} - 3622993920 x^{11} + 71735279616 x^{10} - 1093109022720 x^{9} + 1.29124 E 13 x^{8} - 1 2^{9} \cdot 22880 x^{7} + 8.2639 E 14 x^{6} - 1 2^{11} \cdot 5824 x^{5} + 1.62273 E 16 x^{4} - 3.99441 E 16 x^{3} + 5.13567 E 16 x^{2}) + C

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