Integral of the Day 10.11.24 | Straight from the Integration Bee! | Math with Professor V

Here's your latest Integral of the Day! I attended the annual Integration Bee at the college where I teach yesterday, so I have several fun new integrals to share with you all here. The only integration technique required to solve this is u-substitution! Were you able to solve it?

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Professor V

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[siyabongashoba]

thank you so much for the integral of the day

[tonychow]

Hi Professor V, thank you for your new video. I used the same method as yours, u=x^3x and got the same result. Cheers.

[siyabongashoba]

Dear Prof.V, I hope you are doing well, for this one I tried integration by part and it became very huge when I look at the length of your video it is like 5 minutes and there is a simple way of solving it. and look at the u = x^(3x) and when finding du=3(ln(x)+1)x^(3x)dx which looks the same as the original integral just 3 is the difference. I wrote 1/3*du=(ln(x)+1)x^(3x)dx and integrated on both sides and got 1/3*u + C but since there is an endpoint. At the starting point, the value I got was 1/3*(2^6-1) Let me enjoy the video it has been a long time since linear algebra is killed me but complex numbers are not that hard plus I have an old calculus which covers complex number.

[siyabongashoba]

there is this cool I once did an integral of x^(x/lnx) dx that really behave like e^x.

[Ivan-uuh]

Videos on linear algebra and vector spaces

[tonybluefor]

I started to rewrite x^(3x) as e^(3xln(x)) and then it looked like its derivative was similar to the function to integrate by a factor of 1/3