Quiz from yesterday

KingIra

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Hi all, I just wanted to post and ask for help on a quiz question I had yesterday. The teacher generally does not explain and I'm a little lost. Online integration calculators also will not give help me because he asks for a specific u substitution which the calculator does not present as an option. The question is:

1614619752915.png

I get up to about when I'm substituting in u and du, because I find that du is an unwieldy fraction and I'm not sure what to do with the x3 in the top. According to the integration calculator I consulted, if u had just been (x2+1), then x3 would become (u-1) (which I'm also not sure about how but is not the pressing question).

Thank you for your time!
 

Subhotosh Khan

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Hi all, I just wanted to post and ask for help on a quiz question I had yesterday. The teacher generally does not explain and I'm a little lost. Online integration calculators also will not give help me because he asks for a specific u substitution which the calculator does not present as an option. The question is:

View attachment 25447

I get up to about when I'm substituting in u and du, because I find that du is an unwieldy fraction and I'm not sure what to do with the x3 in the top. According to the integration calculator I consulted, if u had just been (x2+1), then x3 would become (u-1) (which I'm also not sure about how but is not the pressing question).

Thank you for your time!
1614629854000.png

u3 = x2 +1

x2 = u3 -1

[x2](3/2) = [u3 -1](3/2)

x3 = [u3 -1](3/2)

Now show your work regarding dx`\to`du conversion.
 

KingIra

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For dx I got du/((2/3)(x2+1)-(1/3)(2x)). Normally I would just continue to solve but usually the teacher has the questions set up in a way that most if not all of the terms attached to du can be cancelled out or moved, leaving du by itself, so when I wasn't sure of the numerator, I thought maybe I took du incorrectly.
 

KingIra

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3u2du/(2(u3-1)1/2) ?
 

Subhotosh Khan

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3u2du/(2(u3-1)1/2) ?
Correct ... what does the integrand look like?

\(\displaystyle \int \frac{1}{u} * (u^3-1)^{\frac{3}{2}} * \left(\frac{3*u^2}{2} (u^3-1)^{-\frac{1}{2}}\right) du\)

continue......
 

KingIra

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(3/2)∫(u3-1)du ?
 

Subhotosh Khan

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You are missing a 'u'!
 
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