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

tanvidais13
 one year ago
Best ResponseYou've already chosen the best response.0wait i don't need to, its factorizable: \[7/\sqrt{(1+x)(5x)}\]

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

tanvidais13
 one year ago
Best ResponseYou've already chosen the best response.0so we need to complete the square, or do a substitution?

.Sam.
 one year ago
Best ResponseYou've already chosen the best response.3We 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, \[x=asin(\theta), \text{while} ~~~~~ a^2x^2 ~~~~~ \text{is} ~~~~~ 3^2(x2)^2, \\ \\So \\ \\\\\\ x2=3\sin(\theta) ~~~~~ \theta=\sin^{1}(\frac{x}{3}) \\ \\ dx=3\cos (\theta) d \theta \\\\\\\\ 7 \int\limits \frac{3\cos \theta}{\sqrt{3^2(3\sin \theta)^2}}d \theta\]

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

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

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

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

tanvidais13
 one year ago
Best ResponseYou've already chosen the best response.0I love you, you are a life saver. Really.
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