Chloe W.

asked • 02/18/15

Integration by u substitution help

I need to solve the indefinite integral, however it must be by the u - sub method.  
 
∫(x2+2)(x-1)7dx
 
Im guessing this is not the best way, however by tutor tells me it can be done the u sub way. I just can't seen to see how. Would be grateful of any help you good people can offer.
 
chloe

Mitiku D.

Chloe, if you have u=x-1, as indicated by the answer below, you can say that x=u+1, and you substitute that in x2+2 and get (u+1)2+2 = u2+2u+1 +2 = u2+2u+3................... you are better of without substitution. It's much easier to just multiply out the factors (x2+2) and (x-1)7 and integrate
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02/18/15

Michael W.

Sorry, um, you want to multiply out (x-1)7 ???  And then multiply that by x2 + 2?
 
Ooooookay, let's get started!
 
(x - 1)(x - 1) = x2 - 2x + 1
(x2 - 2x +1)(x - 1) = x3 - x2 - 2x2 - 2x + x - 1 = x3 - 3x2 + 3x - 1
 
I think Chloe would be done with the u-substitution version by now, and we've still got four more powers to go.  :)
 
-- Michael
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02/18/15

1 Expert Answer

By:

Michael W. answered • 02/18/15

Tutor
New to Wyzant

Chloe W.

Thank you Michael, like you said normally the piece left over cancels out with the derivative these are the ones i a m used to doing. So with what you have said i have had a go, can you tell me if i have got the correct answer and if not where i have gone wrong?
 
u = x-1, therefore x = u+1. So if we sub this into (x2+2) we get (u+1)2+2, expand brackets to get, u2+2u+1 then add the 2 to get - u2+2u+3.
 
So we now have:  (u2+2u+3) x u7  = u9+2u8+3u7
Now integrate this to get - u10/10 + 2u9/9 +3u8/8 + c
 
Then the final answer will be the above with (x-1) subbed back to replace the u.
 
so: (x-1)10/10 + 2(x-1)9/9 + 3(x-1)8/8 + c
 
Thanks Chloe.
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02/18/15

Michael W.

Looks right to me!  And yes, it seems like you found the integral using the substitution faster than we could have multiplied (x-1) seven times.  :)
 
Nice work.
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02/18/15

Chloe W.

Thank you so much Michael!! Feel a lot more confident now.
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02/18/15

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