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El_Arrow
 one year ago
don't understand how it got that answer please help
El_Arrow
 one year ago
don't understand how it got that answer please help

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El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0i understand the completing the square part i dont understand where the tangent came from

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@freckles @jim_thompson5910 @Zarkon

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}\frac{1}{u^2+1} du =\arctan(u)+C \\ \text{ and you have } \frac{1}{4} \int\limits \frac{dx}{\frac{1}{4}(x+3)^2+1} =\frac{1}{4} \int\limits \frac{dx}{(\frac{1}{2}(x+3))^2+1} \\ \text{ Let } u=\frac{1}{2}(x+3) \\ du=\frac{1}{2} dx\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1One way is to use a table of integrals (if you can recognize the form) http://integraltable.com/ look at equation (9) under the "Integrals of Rational Functions" section

yolomcswagginsggg
 one year ago
Best ResponseYou've already chosen the best response.0...................__ ............./´¯/'...'/´¯¯`·¸ ........../'/.../..../......./¨¯\ ........('(...´...´.... ¯~/'...') .........\.................'...../ ..........''...\.......... _.·´ ............\..............( BROFIST ...........

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@freckles how did you get the 1/2 out front of (x+3)^2?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[a+b=b(\frac{a}{b}+1) \\ \text{ so like here we had } \\ (x+3)^2+4 =4[\frac{1}{4}(x+3)^2+1]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I just factored a 4 out on the bottom

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so (x+3)^2 is a and the 4 is b correct?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[(x+3)^2+4 \\ = \\ \frac{4}{4}(x+3)^2+4 \\ =4 \cdot \frac{1}{4}(x+3)^2+4 \cdot 1 \\ = \\ =4[\frac{1}{4}(x+3)^2+1]\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1yeah in that example yes you can say that which is perfectly fine

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I put a few more lines in between there maybe it to make it more clear hopefully

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0okay thanks @freckles
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