I've only recently started teaching myself Calculus, so you'll have to forgive me if I'm trying to do something silly or impossible. This has been bugging me for a few days, so I figured it's high time I ask someone.(adsbygoogle = window.adsbygoogle || []).push({});

Since we can write [tex]\int_{a}^b f(x)[/tex] as [tex]\int_{a}^b\ e^\ln(f(x))[/tex] would it be possible to use substitution to yank [tex]ln(f(x))[/tex] out of the integral and leave us with

[tex]g(\int_{ln(f(a))}^\ln(f(b))} e^x } )[/tex]

With g(x) as what we pulled out of the integral. I'm very new to integration, but this idea has been puzzling me for a while. If this is possible, it would seem pretty dang handy when integrating. Then again, I'm playing with methods I've only recently taught myself (I came up with this while running on a tredmil, actually.) It's fully possible I misunderstood something or overlooking a rule that makes this impossible. Anyway, thanks for any information that flies my way.

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# An idea for integration that has been bugging me.

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