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

Limits, differentiation, related rates, integration, trig integrals, etc.
mitnord
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Joined: Mon Feb 23, 2009 11:17 pm
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### need to solve integral: Int (6 - 3x)^5 dx

Int(6 -3x)^5 dx

Please show how to solve.

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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Int(6 -3x)^5 dx
Have you learned about u-substitution yet?

Thank you!

FrozenBlood
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Joined: Wed Feb 04, 2009 11:31 pm
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### Re: need to solve integral: Int (6 - 3x)^5 dx

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.