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.Sam.
 2 years ago
@tanvidais13
.Sam.
 2 years ago
@tanvidais13

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

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

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

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

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

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

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