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agentx5
Group Title
I need some help with checking this answer please:
\[\large\int\limits_4^5 \frac{x^33 x^29}{x^33 x^2} dx = x\frac{3}{x}\ln3x+\lnx+C\]
I got this far using the partial fractions technique. I went to check my answer that I got on paper but Wolfram gives some craziness with hyperbolic tangents that I don't understand. So what should the answer be and wouldn't the natural log of 3x be an issue because it gives nonreal values?
The correct answer MUST have real values and be in terms of constants and logs. If somebody could show me what's going on here it would be great :)
 2 years ago
 2 years ago
agentx5 Group Title
I need some help with checking this answer please: \[\large\int\limits_4^5 \frac{x^33 x^29}{x^33 x^2} dx = x\frac{3}{x}\ln3x+\lnx+C\] I got this far using the partial fractions technique. I went to check my answer that I got on paper but Wolfram gives some craziness with hyperbolic tangents that I don't understand. So what should the answer be and wouldn't the natural log of 3x be an issue because it gives nonreal values? The correct answer MUST have real values and be in terms of constants and logs. If somebody could show me what's going on here it would be great :)
 2 years ago
 2 years ago

This Question is Closed

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
For my partial fractions I got: \[x^33x^29=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x3}\] The A part turns into lnx, the B part turns into 3/x, the C part turns into ln3x
 2 years ago

helder_edwin Group TitleBest ResponseYou've already chosen the best response.1
\[ \Large \int\frac{x^33x^29}{x^33x^2}\,dx= \int\,dx\int\frac{9}{x^2(x3)}\,dx \] so you have to solve \[ \Large \frac{9}{x^2(x3)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x3} \]
 2 years ago

Valpey Group TitleBest ResponseYou've already chosen the best response.0
Well, for one thing you have written the natural log of the absolute value of 3x.
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Yeah I used long division initially to pull out this: \[1 + \frac{9}{x^33x^2}\]
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Integral of one with respect to x is just x, logically
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
I think I mistyped my second post, sry @helder_edwin
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
@Valpey oh yeah... so it's always a positive...
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
ln3(4) = ln1 = ln 1 = 0
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
That's a nice simplification
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
/me waves hello @asnaseer :) ty for stopping by!
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
you didn't need to do long division to simplify this in the first place. you could just have done this:\[\frac{x^33x^29}{x^33x^2}=\frac{x^33x^2}{x^33x^2}\frac{9}{x^33x^2}=1\frac{9}{x^33x^2}\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
secondly, the logs should not contain the absolute value symbols around them
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Good point @asnaseer and why not? Without it wouldn't I have a nonreal answer issue when I go to evaluate?
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
you should have done this:\[\int\limits_4^5 \frac{x^33 x^29}{x^33 x^2} dx =[ x\frac{3}{x}\ln(3x)+\ln(x)]_4^5\]\[\qquad=[x\frac{3}{x}+ln(\frac{x}{3x})]_4^5\]\[\qquad=(5\frac{3}{5}+ln(\frac{5}{2}))(4\frac{3}{4}+ln(\frac{4}{1}))\]\[\qquad=5\frac{3}{5}4+\frac{3}{4}+ln(\frac{5}{2}\div\frac{4}{1})\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
and the minuses cancel out inside the logs
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
*reading carefully*
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
BTW: waves hello back to @agentx5 :)
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Oh... properties of logs... \[\lna\lnb=\ln\frac{a}{b}\]
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
yes  but you shouldn't use the '' symbols here
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
as they usually indicate absolute value
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
\[\qquad=5\frac{3}{5}4+\frac{3}{4}+ln(\frac{5}{2}\div\frac{4}{1}) \approx 3.45258\] Disagrees with this check: http://www.wolframalpha.com/input/?i=integrate+from+4+to+5+for+%28x^33x^29%29%2F%28x^33x^2%29 \(\approx \frac{17}{25}\)
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
I work it out to be exactly the same as the answer wolfram gives
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
I get:\[\frac{23}{20}+ln(\frac{5}{8})\approx 0.68\]
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Ugh I see now I used the wrong base log on my calculator... /facepalm
 2 years ago

agentx5 Group TitleBest ResponseYou've already chosen the best response.0
Thank you so much you were a great help! @TuringTest give that claymationman a medal ^_^
 2 years ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.2
you are more than welcome my friend! :)
 2 years ago
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