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SmartyPants's latest activity
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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##\sin x \cos 2x = \frac12 (\sin 3x - \sin x)## - this is the trig manipulation I used to get to the final solution. And thank you for...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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Yes, it's a bug. It only calculates \int \sin x \cos 2x\,dx by integrating by parts twice; the \ln (x) is completely ignored. It's not...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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Right, but differentiating the two results and arriving at the same integrand should convince you that the technique chosen by Math DF...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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Hmm...I doctored that image to show the entire equation before posting it...weird that it's not showing you the entire equation. At any...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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##\ln |\sec(x)| = \ln \frac 1{|\cos(x)|} = -\ln|\cos(x)|## In this case, the different results are exactly equal. Seems to me that it...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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Yes. For a different example, for the indefinite integral ##\int \sin(x)dx##, both ##\frac 1 2 \sin^2(x) + C## and ##-\frac 1 2...
Apr 5, 2024
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SmartyPants
replied to the thread
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Did Math DF's integral calculator make a glaring mistake?
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Agreed...but even if I could show that two different antiderivatives have the same derivative, that doesn't help me understand how Math...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
.
Thanks for clarifying that much Mark. That makes much more sense, as I don't know that ##ln\left | sec~x \right |## (an antiderivative...
Apr 5, 2024
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SmartyPants
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Did Math DF's integral calculator make a glaring mistake?
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Calculus
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In calculating the integral ##\int{\ln\left(x\right)\,\sin\left(x\right)\,\cos\left(2\,x\right)}{\;\mathrm{d}x}##, I used a few online...
Apr 5, 2024
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