indefnite integral

Link88 · #1 $Old$ 12-01-2008, 07:40 PM

Im not sure if this answer is right and wanted to see what you guys could get. 2x/Sqrt(1+x^4) dx Answer=ln(Sqrt(1+x^4+x^2)+C. Thanks.

Chop Suey · #2 $Old$ 12-01-2008, 07:49 PM

Well, one way is to notice that:
$\int \frac{2x}{\sqrt{1+(x^2)^2}}~dx$

Try a trigonometric substitution such as $x^2=\tan{u}$ which yields $2x~dx = \sec^2{u}~du$ . You eventually end up with:

$\int \sec{u}~du = \ln{|\sec{u}+\tan{u}|}+C$

Don't forget to back-substitute.