Question

integral(1/(xsqrt(1+ln(x)^2)dx

Answer 1

\[\int\limits \frac{ 1 }{ x \sqrt{1+\ln^2} }dx\]

Answer 2

u=ln(x) du=1/xdx dx=xdu

Answer 3

\[\int\limits \frac{ 1 }{ \sqrt{1+u^2}}du\]

Answer 4

we can't use the identity so do I have to do a trig sub for this?

Answer 5

u=sin(theta) dx=cos(theta)

Answer 6

but when I try this:
\[\int\limits\frac{ 1 }{ \sqrt{1+\sin^2}(\theta) }\cos(\theta)d(\theta)\]

Answer 7

and simplify i get down to
\[\int\limits \frac{ 1 }{ \cos(\theta) }\cos(\theta)d(\theta)\]

and
\[\int\limits1d(\theta)\]

Answer 8

i get stuck

Answer 9

what is arcsinh?

Answer 10

inverse hyperbolic function and arcsinhx = log (x+sqrt(x^2+1))

Source: http://www.mathskey.com/question2answer/