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Popular >

integral of x(x-4)^8

Solution

\int x (x - 4)^{8} d x

Solution

\frac{1}{2} x^{2} (x - 4)^{8} - 4 (\frac{x ^{10}}{10} - \frac{28 x ^{9}}{9} + 42 x^{8} - 320 x^{7} + \frac{4480 x ^{6}}{3} - \frac{21504 x ^{5}}{5} + 7168 x^{4} - \frac{16384 x ^{3}}{3}) + C

Solution steps

\int x (x - 4)^{8} d x

Apply Integration By Parts

: \frac{1}{2} x^{2} (x - 4)^{8} - \int 4 x^{2} (x - 4)^{7} d x

= \frac{1}{2} x^{2} (x - 4)^{8} - \int 4 x^{2} (x - 4)^{7} d x

\int 4 x^{2} (x - 4)^{7} d x = 4 (\frac{x ^{10}}{10} - \frac{28 x ^{9}}{9} + 42 x^{8} - 320 x^{7} + \frac{4480 x ^{6}}{3} - \frac{21504 x ^{5}}{5} + 7168 x^{4} - \frac{16384 x ^{3}}{3})

= \frac{1}{2} x^{2} (x - 4)^{8} - 4 (\frac{x ^{10}}{10} - \frac{28 x ^{9}}{9} + 42 x^{8} - 320 x^{7} + \frac{4480 x ^{6}}{3} - \frac{21504 x ^{5}}{5} + 7168 x^{4} - \frac{16384 x ^{3}}{3})

Add a constant to the solution

= \frac{1}{2} x^{2} (x - 4)^{8} - 4 (\frac{x ^{10}}{10} - \frac{28 x ^{9}}{9} + 42 x^{8} - 320 x^{7} + \frac{4480 x ^{6}}{3} - \frac{21504 x ^{5}}{5} + 7168 x^{4} - \frac{16384 x ^{3}}{3}) + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x(x-4)^8 ?
The integral of x(x-4)^8 is