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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 :)
 one year ago
 one year ago
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 :)
 one year ago
 one year ago

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agentx5Best 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
 one year ago

helder_edwinBest 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 \[ \Large \frac{9}{x^2(x3)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x3} \]
 one year ago

ValpeyBest ResponseYou've already chosen the best response.0
Well, for one thing you have written the natural log of the absolute value of 3x.
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
Yeah I used long division initially to pull out this: \[1 + \frac{9}{x^33x^2}\]
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
Integral of one with respect to x is just x, logically
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
I think I mistyped my second post, sry @helder_edwin
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
@Valpey oh yeah... so it's always a positive...
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
ln3(4) = ln1 = ln 1 = 0
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
That's a nice simplification
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
/me waves hello @asnaseer :) ty for stopping by!
 one year ago

asnaseerBest 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:\[\frac{x^33x^29}{x^33x^2}=\frac{x^33x^2}{x^33x^2}\frac{9}{x^33x^2}=1\frac{9}{x^33x^2}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
secondly, the logs should not contain the absolute value symbols around them
 one year ago

agentx5Best 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?
 one year ago

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

asnaseerBest ResponseYou've already chosen the best response.2
and the minuses cancel out inside the logs
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
BTW: waves hello back to @agentx5 :)
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
Oh... properties of logs... \[\lna\lnb=\ln\frac{a}{b}\]
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
yes  but you shouldn't use the '' symbols here
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
as they usually indicate absolute value
 one year ago

agentx5Best 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 \(\approx \frac{17}{25}\)
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
I work it out to be exactly the same as the answer wolfram gives
 one year ago

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

agentx5Best ResponseYou've already chosen the best response.0
Ugh I see now I used the wrong base log on my calculator... /facepalm
 one year ago

agentx5Best ResponseYou've already chosen the best response.0
Thank you so much you were a great help! @TuringTest give that claymationman a medal ^_^
 one year ago

asnaseerBest ResponseYou've already chosen the best response.2
you are more than welcome my friend! :)
 one year ago
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