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## Main Question or Discussion Point

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.

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.

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.