I want to solve this integral. For integration by substitution, I let $$\frac{d}{dt}f(t)=\tan\theta.$$ But, I cannot solve for $f(t)$ and $\frac{d^2}{dt^2}f(t)$. I cannot even find $\frac{dt}{d\theta}$.
Can anyone help me?
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this $\sqrt{(f'(t))^2+1}^3$ – qmoi Jun 10 '23 at 07:21
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$(f'(t)^2+1)^{3/2}$ ? – NN2 Jun 10 '23 at 07:23
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yes, that's right!! – qmoi Jun 10 '23 at 07:27
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Maybe integration by parts helps after separating the integral. – Bob Dobbs Jun 10 '23 at 07:42