∫√(1+θ^2)dθ=θ√(1+θ^2) - ∫[θ^2/√(1+θ^2) ]dθ
=θ√(1+θ^2) - ∫√(1+θ^2) dθ + ∫dθ/√(1+θ^2)
2∫√(1+θ^2)dθ = θ√(1+θ^2) + ∫dθ/√(1+θ^2)
∫√(1+θ^2)dθ = (1/2)[ θ√(1+θ^2) + ∫dθ/√(1+θ^2) ]
let
θ=tanx
dθ = (secx)^2dx
∫dθ/√(1+θ^2)
=∫secx dx
=ln|secx+tanx| + C'
=ln|√(1+θ^2) +θ| + C'
∫√(1+θ^2)dθ = (1/2)[ θ√(1+θ^2) + ∫dθ/√(1+θ^2) ]
=(1/2)[ θ√(1+θ^2) + ln|√(1+θ^2) +θ| ] + C