That's a very interesting solution! The integrand itself reminds me a lot of an indefinite integral I was doing the other day. It was ∫ln(x)e^x dx, which looks somewhat similar to this video's problem but is obviously a bit different. I had to use u-sub, IBP (I used the DI method), the Logarithmic Integral Function li(x), and the Exponential Integral Function Ei(x) all in that order. It was very interesting and very fun. I highly recommend!
@@wryanihad IBP and the DI method tends to work well with the following products as the integrand: Exponentials and trig Exponentials and polynomials Trig and polynomials Trig, polynomials, and exponentials in a 3-term product Algebraic and inverse trig Algebraic and logs Logs and special cases of inverse trig You run into trouble trying to make it work for logs and exponentials, or inverse trig and exponentials, as you'll end up with integrals that have no elementary solution. This is why it's very difficult to use it for the Laplace transform of functions other than exponentials, trig, and polynomials, and you end up needing alternative methods.
Nice solution, can’t get enough of seeing Feynman’s trick over and over
Good to hear! Sometimes I worry people will get sick of the same technique 😆
Thanks!
Hi William. Thank you! Appreciate the “super thanks” comment!! 😃🙏
That's a very interesting solution!
The integrand itself reminds me a lot of an indefinite integral I was doing the other day. It was ∫ln(x)e^x dx, which looks somewhat similar to this video's problem but is obviously a bit different. I had to use u-sub, IBP (I used the DI method), the Logarithmic Integral Function li(x), and the Exponential Integral Function Ei(x) all in that order. It was very interesting and very fun. I highly recommend!
Hi Lemon thanks!!
Can we solve it by D I method
@@wryanihad I don't think so but I didn't try it. I think it sort of goes around in circles and would be difficult.
@@wryanihad IBP and the DI method tends to work well with the following products as the integrand:
Exponentials and trig
Exponentials and polynomials
Trig and polynomials
Trig, polynomials, and exponentials in a 3-term product
Algebraic and inverse trig
Algebraic and logs
Logs and special cases of inverse trig
You run into trouble trying to make it work for logs and exponentials, or inverse trig and exponentials, as you'll end up with integrals that have no elementary solution. This is why it's very difficult to use it for the Laplace transform of functions other than exponentials, trig, and polynomials, and you end up needing alternative methods.
@@carultchwhat are some examples of algebraic functions?
You weren't kidding. That was great!
Hey Mike. Thanks! Nice problem today. 😃
❤
Thanks 🙏😃