sqrt(1 +a^2*x^2) dx
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You want to do a trig substitution so that the square root term will disappear. Have you tried subbing tangent, secant, cotangent, or cosecant in for x?
i have been trying x = a*sinh u
Originally Posted by j-lee00 i have been trying x = a*sinh u Try
Originally Posted by j-lee00 i have been trying x = a*sinh u should work.
Hello, j-lee00! Integrate: .
This integral requires Integration By Parts twice, or a standard formula. . .
Back-substitute . . .
I didn't work with the geometry, but Soroban basically completed what I started for you.
J Lee was trying to use a sinh substitution; I think the integration is easier with this substitution.
Now you can substitute the x back (noting that
thanks for all your assistances
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