Integrals :)

Question

Integrals :)

sleepyjess · Answer

$$\int\limits 8(x+x^2)^{-1}~dx$$

sleepyjess · Answer

Would I distribute the 8 first?

nnesha · Answer

$$\int\limits_{ }^{ } \frac{8}{x(1+x^2)} dx $$

johnweldon1993 · Answer

I would just move the 8 out of the integral :) It's just a constant

amorfide · Answer

wouldn't that be x(1+x) on the bottem nnesha

sleepyjess · Answer

Whoops, that was supposed to be 1+x^2

solomonzelman · Answer

$\displaystyle \int \frac{8}{x^2+1} dx$.   Trig sub.

solomonzelman · Answer

or just recon the derivative of what may the integrand be?

solomonzelman · Answer

(You have done the derivatives of inverse trig functions, haven't ya?)

sleepyjess · Answer

Yes, we've done inverse sine, tangent and secant

solomonzelman · Answer

Yes ... more is not requered.

sleepyjess · Answer

Oohhh, I think I see, it would be 8$tan^{-1}x + c$?

solomonzelman · Answer

Do you remember the inverse derivative of $\arcsin(x)$, ${\rm arcsec}(x)$, and $\arctan(x)$?

solomonzelman · Answer

did I just say INVERSE DERIVATIVE ?? OMG ...
Just derivative (not inverse derivative)

solomonzelman · Answer

yes, you are thinking correctly:)

sleepyjess · Answer

We haven't done any of those 3...

solomonzelman · Answer

Though, if you want to actually solve it, as opposed to realizing the derivative, you may choose to ask for more assistance.  (If you learned trig sub, I would advise that, if not, don't worry right now, you will cover it later.)

sleepyjess · Answer

We haven't gotten into that yet, just started integrals today :)

solomonzelman · Answer

Oh today ... you are getting tuned in very quickly then.
Keep it up!