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Popular Calculus >

integral of (2x-5)^{11}

Solution

\int (2 x - 5)^{11} d x

Solution

(2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2}) + C

Solution steps

\int (2 x - 5)^{11} d x

Apply Integration By Parts

= (2 x - 5)^{11} x - \int 22 (2 x - 5)^{10} x d x

\int 22 (2 x - 5)^{10} x d x = 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2})

= (2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2})

Add a constant to the solution

= (2 x - 5)^{11} x - 22 (\frac{256 x ^{12}}{3} - \frac{25600 x ^{11}}{11} + 28800 x^{10} - \frac{640000 x ^{9}}{3} + 1050000 x^{8} - 3600000 x^{7} + 8750000 x^{6} - 15000000 x^{5} + 17578125 x^{4} - \frac{39062500 x ^{3}}{3} + \frac{9765625 x ^{2}}{2}) + C

Graph

Popular Examples

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x^{^{'}} = 6 c_{1} - \frac{3 x}{5}

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Frequently Asked Questions (FAQ)

What is the integral of (2x-5)^{11} ?
The integral of (2x-5)^{11} is