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What solution $$\int\sqrt{1+(-2ax+b)^2}\;dx$$Unable to develop anything ...$~$:'( I tried completing squares, but can not move much.
2026-04-11 19:30:25.1775935825
Solving $\int\sqrt{1+(-2ax+b)^2}\;dx$
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The substitution $u = -2ax+b$ will get rid of the expression inside the square, so you might as well be dealing with $\int \sqrt{1+u^2}\ du$. This is a very common integral; you can solve it substituting either $u = \tan t$ or $u = \sinh t$.