Question

See if you guys can integrate this :)
∫3/(x^2+2) dx

Answer 1

\[\int\limits_{}^{} \frac{3}{x ^{2}+2} dx\]

Answer 2

\[\int \frac{3}{x^2+2} dx\]
\[x= \sqrt {2} \tan \theta\]
\[dx=\sqrt{2} \sec^2 \theta\]
\[\int3 \sqrt{2}\sec^2 \theta \frac{d\theta }{2\tan^2\theta+2}\]
\[\int 3\sqrt{2} \sec^2 \theta \frac{d\theta}{2 \sec^2\theta}\]
we get
\[\int 3 \sqrt{2} \frac{d\theta}{2}\]
we get
on integration
\[ \frac{3}{\sqrt{2}} \theta+C\]
we have
\[ \tan \theta= \sqrt{2} x\]
\[\theta = \tan ^{-1} (\sqrt {2} x)\]
so we get
\[ \frac{3}{\sqrt{2}}\tan ^{-1} (\sqrt {2} x)+ C \]

Answer 3

we have
x^2+2 in the denominator
if \[x= \sqrt {2} x\]
then
\[ x^2+2= 2 \tan^2 \theta +2= 2(\tan^2 \theta +1)= 2 \sec^2 \theta\]
also
\[dx =\sqrt {2} \sec^2 \theta\]
so the \(\sec^2 \theta \) gets cancelled from numerator and denominator, we 're left with an easy integration.

Answer 4

hey sam can you help? x^2+18x+4=0

Answer 5

it ask to put it in a quadratic form