Question

integral of sqrt(1+x^2)/x^2

Answer 1

What do you think you can do?

Answer 2

trig substitution probably.

Answer 3

Yes. The identity of 1 + tan^2(x) applies. How do you substitute x = tan(x)?

Answer 4

sub x = tanx, then dx = \[\sec ^{2}x\]
Then:
int of \[\sqrt(1+x^2)/x^2\] = \[(\sqrt(\tan^2x + 1)(\sec^2x)/\tan^2x)\]
= \[\int\limits_{}^{} \sec^3x/\tan^2x. \]
Not sure what to do now.

Answer 5

Um, sqrt(tan^2(x)+ 1) = sec(x), not sec^2(x).
Anyway, sec(x) = 1/cos x, tan x = sin x / cos x. Substitute.

Answer 6

Nevermind, I see your logic.

Answer 7

Or do I?

Answer 8

\[\sec^2x\] is from the dx. dx = sec^2x

Answer 9

Yeah, thought so. Continue.

Answer 10

\[\int\limits_{}^{}(1+\tan^2x(secx))/\tan^2x = \int\limits_{}^{} secx/tanx + secxtan^2x/\tan^2x = \int\limits_{}^{} secx/tanx + secx = \int\limits_{}^{} sinx/\cos^2x + secx = 1/cosx + \ln \left| secx + tanx \left| \right| \right|\]

Answer 11

how do you make the screen bigger