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by **mitnord** on Wed Mar 11, 2009 10:52 pm

Int(6 -3x)^5 dx

Please show how to solve.

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by **stapel_eliz** on Thu Mar 12, 2009 2:31 am

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

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

Thank you!

by **FrozenBlood** on Thu Mar 12, 2009 7:44 pm

U-substitution is exactly the way to go.

First off, you have:

$\int (6 - 3x)^5 dx$

Now, let $u = 6 - 3x$ , so that $du = -3dx$ . Then $dx = -\frac{1}{3}du$ .

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

$-\frac{1}{3}\int u^5 du$

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

$-\frac{1}{18}u^6 + C$

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

$-\frac{1}{18}(6 - 3x)^6 + C$

That's all.

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

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

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