Question

Trig Substitution: I have sovled it a little but am unsure of where to go

Answer 1

\[\int\limits dx/x^2\sqrt(x^2+1)\]

Answer 2

i got to an integral of (sec(theta)/tan^2(theta) but idk where to go from here

Answer 3

hmmm, you sure its typed in correctly?

Answer 4

x^2 + 1 suggests a tangent for x


x = tan t
dx = sec^2 dt

\[\int \frac{sec^2}{tan^2sec}dt \]
\[\int \frac{sec}{tan^2}dt \]
\[\int cot^2sec\ dt \]
\[\int \frac{sin^2}{cos^3}\ dt \]
something along those lines maybe

Answer 5

ya i got to that point as well but i dont know how to take the integral of that

Answer 6

sec2 cot2 cos

cos cos
cos sin sin

cot csc

Answer 7

that might be doable

Answer 8

just missing a - to make it up to csc

Answer 9

sooo,

-csc + C



csc = sqrt(x^2+1)/x

Answer 10

how did you get the stuff in the sec2 cot2 cos post?

Answer 11

i stared at it till it made sense :)

we got to:\[\frac{sec^2}{tan^2sec}\]
so i split it up into its sin cos parts to see what i could construct
\[\large \frac{\frac{1}{cos}\frac{1}{cos}}{\frac{sin}{cos}\frac{sin}{cos}\frac{1}{cos}}\]
\[\large \frac{1}{cos}\frac{1}{cos}\frac{cos}{sin}\frac{cos}{sin}\frac{cos}{1}\]
\[\large \frac{}{}\frac{}{}\frac{}{sin}\frac{}{sin}\frac{cos}{}\]
\[\frac{cos}{sin}\frac{1}{sin}=cot\ csc\]