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anonymous
 4 years ago
evaluate the following: integral S (e^3x)/((e^6x)+1) dx
(hint: u=e^3x)
anonymous
 4 years ago
evaluate the following: integral S (e^3x)/((e^6x)+1) dx (hint: u=e^3x)

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Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.5\[u=e^{3x} \implies du=3e^{3x}dx\] \[I=\frac{1}{3}\int \frac{du}{u^2+1}=\frac{1}{3}\tan^{1}u+c=\frac{1}{3}\tan^{1}(e^{3x})+c.\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}\frac{e^{3x}}{e^{6x}+1} dx\] Thinking.... \[e^{3x}=\tan(\theta)\] => dang it

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.5Obviously \(I\) is the integral you gave.

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.5@myin: My substitution was a hint from the question :D

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}\frac{ \frac{1}{3} \sec^2(\theta)}{\tan^2(\theta)+1} d \theta\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.1it contains both subs

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0haha that's awesome. i knew it was (1/3)arctan(e3x) + C. i was just seeing if this actually worked :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits \frac{e^{3 x}}{1+e^{6 x}} \, dx=\frac{1}{3} \text{ArcTan}\left[e^{3 x}\right]+c \]
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