Question 1121154: Find integral (dx/sqr(x^2+16)) Found 3 solutions by Alex.33, solver91311, Edwin McCravy:Answer by Alex.33(110) (Show Source): You can put this solution on YOUR website! https://www.symbolab.com/solver/step-by-step/%5Cint%5Cleft(%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%5E%7B2%7D%2B16%7D%7D%5Cright)dx
check this out. This may solve your problem. If you have any question about the proofs of the specific formulae, just ask the search engines-there are abundant of them awaiting.
Special mention: it seems that your question turns out to be arcsinh(x/4) on Methematica. But it seems that the result given by the two sites are equivalent. I derived both using both tools, and got the same result. Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website! Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website! Find integral (dx/sqr(x^2+16))
We use trig substitution by drawing this right triangle:
Then and
So
and
Substituting, becomes
Cancel and get
We use
Use trig ratios from above right triangle:
We let to simplify and end up with:
Edwin