#int 1/sqrt(e^(2x)-2e^x+10)dx#
#int (e^xe^-x)/sqrt(e^(2x)-2e^x+10)dx#
#t = e^x#
#dt = e^x#
#int 1/(tsqrt(t^2-2t+10))dt#
#int 1/(tsqrt(t^2-2t+1 + 9))dt#
#int 1/(tsqrt((t-1)^2 + 9))dt#
#t-1 = 3tan(u)#
#dt = 3(tan^2(u)+1)du#
#(t-1)^2 = 9tan^2(u)#
#int 1/(tsqrt((t-1)^2 + 9))dx#
#int(3/cos^2(u))/((3tan(u)+1)(3/cos(u))) du#
#int(3/cos^2(u))/((9sin(u)/cos^2(u)+3/cos(u))) du#
#int1/((3sin(u)+cos(u))) du#
#w = tan(u/2)#
#3sin(u) = (6w)/(w^2+1)#
#cos(u) = (1-w^2)/(w^2+1)#
#du = (2dw)/(w^2+1) #
#int(2/(w^2+1))/(((6w)/(w^2+1)+(1-w^2)/(w^2+1))) dw#
#int2/(6w+1-w^2) dw#
#-int2/(w^2-6w+9-10) dw#
#-2int1/((w-3)^2-10) dw#
#sqrt(10)v = (w-3)#
#sqrt(10)dv = dw#
#-2sqrt(10)/10int1/(v^2-1) dv#
#-2sqrt(10)/10[arctanh(v)]+C#
#-2sqrt(10)/10[arctanh((tan(arctan((e^x-1)/3)/2)-3)/sqrt(10))]+C#