Question

How do you integrate `x(x-1)^6 dx`?

Answer 1

`int x(x-1)^6 dx = 1/8(x-1)^8+1/7(x-1)^7+C`

Explanation:

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`x(x-1)^6 = (x-1+1)(x-1)^6 = (x-1)^7 + (x-1)^6`

So:

`int x(x-1)^6 dx = 1/8(x-1)^8+1/7(x-1)^7+C`