What is the integral of x(2x-5)^5 ?

The integral of x(2x-5)^5 is 1/12 x(2x-5)^6-1/168 (2x-5)^7+C

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integral of x(2x-5)^5

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

\frac{1}{12} x (2 x - 5)^{6} - \frac{1}{168} (2 x - 5)^{7} + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{12} x (2 x - 5)^{6} - \int \frac{1}{12} (2 x - 5)^{6} d x

\int \frac{1}{12} (2 x - 5)^{6} d x = \frac{1}{168} (2 x - 5)^{7}

= \frac{1}{12} x (2 x - 5)^{6} - \frac{1}{168} (2 x - 5)^{7}

Add a constant to the solution

= \frac{1}{12} x (2 x - 5)^{6} - \frac{1}{168} (2 x - 5)^{7} + C

What is the integral of x(2x-5)^5 ?
The integral of x(2x-5)^5 is 1/12 x(2x-5)^6-1/168 (2x-5)^7+C