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.Sam.Best ResponseYou've already chosen the best response.3
Your question \[\int\limits \frac{7}{\sqrt{5+4xx^2}}\] Try completing the square @tanvidais13
 one year ago

tanvidais13Best ResponseYou've already chosen the best response.0
wait i don't need to, its factorizable: \[7/\sqrt{(1+x)(5x)}\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
no you can't do that because we can't use partial fractions here
 one year ago

tanvidais13Best ResponseYou've already chosen the best response.0
so we need to complete the square, or do a substitution?
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
We can try using trig substitution, it might work, so if we complete the square then we got \[\int\limits\limits \frac{7}{\sqrt{9(x2)^2}} \, dx\] Put it like this, \[\int\limits\limits\limits \frac{7}{\sqrt{3^2(x2)^2}} \, dx\] Using trig sub, \[x=asin(\theta), \text{while} ~~~~~ a^2x^2 ~~~~~ \text{is} ~~~~~ 3^2(x2)^2, \\ \\So \\ \\\\\\ x2=3\sin(\theta) ~~~~~ \theta=\sin^{1}(\frac{x}{3}) \\ \\ dx=3\cos (\theta) d \theta \\\\\\\\ 7 \int\limits \frac{3\cos \theta}{\sqrt{3^2(3\sin \theta)^2}}d \theta\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
\[7 \int\limits \frac{3\cos \theta}{\sqrt{3^2(1\sin^2 \theta)}}d \theta \\ \\ \text{We know that} \sqrt{ab}=\sqrt{a} \sqrt{b}\\ \\ 7 \int\limits \frac{\cos \theta}{\sqrt{(1\sin^2 \theta)}}d \theta \\ \\ 7 \int\limits \frac{\cos \theta}{\sqrt{\cos^2 \theta}}d \theta \\ \\7 \int\limits 1 d \theta\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
\[7 \theta +c \\ \\ 7\sin^{1}(\frac{x2}{3}) +c\]
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
Note that theta is\[\theta=\sin^{1}(\frac{u}{3})\] and u=x2
 one year ago

.Sam.Best ResponseYou've already chosen the best response.3
@tanvidais13 Both completing the square and substitution needed
 one year ago

tanvidais13Best ResponseYou've already chosen the best response.0
I love you, you are a life saver. Really.
 one year ago
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