need to solve integral: Int (6 - 3x)^5 dx

Limits, differentiation, related rates, integration, trig integrals, etc.
mitnord
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need to solve integral: Int (6 - 3x)^5 dx

Postby mitnord » Wed Mar 11, 2009 10:52 pm

Int(6 -3x)^5 dx

Please show how to solve.

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stapel_eliz
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Postby stapel_eliz » Thu Mar 12, 2009 2:31 am

mitnord wrote:Int(6 -3x)^5 dx

Have you learned about u-substitution yet? :?:

Thank you! :D

FrozenBlood
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Re: need to solve integral: Int (6 - 3x)^5 dx

Postby FrozenBlood » Thu Mar 12, 2009 7:44 pm

U-substitution is exactly the way to go.

First off, you have:



Now, let , so that . Then .

Put this all back into the original integral, factoring out the -1/3 since it's a constant. This leaves you with:



Integrating that with respect to u gives you this (don't forget to multiply through by the -1/3):



Now replace the u with 6 - 3x, giving you a final answer of:



That's all.


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