# Integral of e^(pi*x)

## Метаданные

- **Канал:** The Math Sorcerer
- **YouTube:** https://www.youtube.com/watch?v=osYl8HJ-TJA
- **Дата:** 03.06.2026
- **Длительность:** 1:22
- **Просмотры:** 1,152
- **Источник:** https://ekstraktznaniy.ru/video/52058

## Описание

We do a simple integral using substitution. I hope this helps someone learning Calculus.
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## Транскрипт

### Integrate e^(pi*x) []

Integrate e to the pi x. So, if it was just e to the x, we would get e to the x because we all know that the integral of e to the x is e to the x plus a constant. So, we have to deal with the pi. To do that, we simply let u be equal to pi x. And then we differentiate both sides here. So, du is equal to pi dx. And now we don't have a pi here in the integrand. So, we have to eliminate it here because this has to look like this. That's the goal. Whenever you get to this step, you want to make this piece here look like what's up here. So, we'll divide both sides by pi. So, we get 1 over pi du is equal to dx. All right, now we're good to go. This is equal to Well, dx is simply 1 over pi du. This is And we have e to the Well, what's pi x? That's u. And now we're in a good place. Now we can integrate. We know that the integral of e to the u is e to the u. So, this is 1 over pi e to the u plus our constant. But, we are not done, right? Because u is equal to pi x. This is 1 over pi e to the pi x plus our constant of integration. And that's it, my friends. If you enjoyed this content, check out my books and courses. Links in the description. Subscribe, like, share, all that good stuff you're supposed to do. Stay strong.