More integrals :)

Question

More integrals :)

babynini · Answer

$$\int\limits_{}^{}\frac{ 1 }{ x^2+6x+14 }$$ I rewrote this as $$\int\limits_{}^{}\frac{ 1 }{ (x+3)^2+5 }$$ but I am not sure that is helpful?

hartnn · Answer

sure it is.
$\int \dfrac{1}{x^2+a^2}dx = \dfrac{1}{a} arctan x +c$

babynini · Answer

but we can't square the 5! unless we write it sqrt5^2

babynini · Answer

is that legal? o_o

hartnn · Answer

i meant
$\int \dfrac{1}{x^2+a^2}dx = \dfrac{1}{a} arctan (x/a) +c$


and yes it is

hartnn · Answer

a = $\sqrt a^2 $

babynini · Answer

wooah
$$\frac{ 1 }{ \sqrt5 }\tan^{-1} (\frac{ x+3 }{ \sqrt5 })+C$$

hartnn · Answer

$\Huge  \checkmark  $

babynini · Answer

that's it? that's the end? :o

hartnn · Answer

absolutely

hartnn · Answer

when i do
$\checkmark$
assume its the end :P

babynini · Answer

xD ik ik but it was so short haha

hartnn · Answer

completing the square was the majority of it, which you had already done :)

babynini · Answer

Well yay! :>
I guess we could rewrite this
$$\frac{ \sqrt5 }{ 5 }\tan^{-1}(\frac{ \sqrt5(x+3) }{ 5 }+C$$ but that doesn't make much of a difference xD

hartnn · Answer

it does,
it makes the answer look more ugly :P

babynini · Answer

*sniffle. fiiine.

hartnn · Answer

onto next one! :)