How do I answer this substitution question?

Question

Evaluate the following indefinite integral using the substitution u=3x-7.

∫ -10/(3x-7)^8 dx = _________

Answer 1

Start by making the integral a bit easier by moving the "-10" outside the integral:

-10∫1/(3x - 7)⁸ dx

If u = 3x - 7 then, by taking the derivative, du/dx = 3 meaning that du = 3dx or that dx = du/3

So substituting "u" for "3x - 7" and "du/3" for "dx" our new integral is:

-10∫1/u⁸ • du/3 and then, again to make it simpler, move the 1/3 outside the integral to get:

-10/3∫1/u⁸ du = -10/3∫u^-8 du

Then you can perform the integral operation and get:

-10/3(-1/7•u^-7 + C)

(10/21)u^-7 + C or 10/(21u⁷) + C

Now, plug "3x - 7" back into the solution you got:

10/(21(3x - 7)⁷) + C