Differentiate x, integrate e^x.
#Integration by parts DI method
royal dawn
Differentiate `x`, integrate `e^x`.
oh woops e^5x sry
unique summitBOT
kangaroo rat
slim skiff
...do you mean xe^(5x)?
royal dawn
...do you mean `xe^(5x)`?
yes
slim skiff
Okay... same answer.
And I don't see how that's any harder to figure out.
If one of the two functions goes to 0 when you differentiate it enough and the other function is one you know how to integrate at all, you always differentiate the function that goes to 0.
royal dawn
oh
thanks
/close
@slim skiff When you integrate e^5x it is 1\5 e^5x You need integration by parts for that and a video I watched said if you need to use integration by parts for integration by parts don't integrate what you were integrating to get integration by parts. What do I do?
slim skiff
<@352737152154468352> When you integrate e^5x it is 1\5 e^5x You need integratio...
You don't need integration by parts for e^(5x). You need u substitution.
Why do you think you would need integration by parts? Integration by parts is for a product of functions.
Not a composition of functions.
royal dawn
You don't need integration by parts for `e^(5x)`. You need u substitution.
you don't but when you integrate that you get 1\5 e^5x which I think you do Need integration by parts for.
slim skiff
you don't but when you integrate that you get 1\5 e^5x which I think you do Need...
Why?
slim skiff
Okay, let's do an experiment. Integrate (1/5)e^(5x) by parts, differentiating 1/5.
royal dawn
Okay, let's do an experiment. Integrate `(1/5)e^(5x)` by parts, differentiating ...
this is what i got
slim skiff
this is what i got
Right, notice something?
royal dawn
yes
the integral of e^5x is exactly what the question was
what does it mean when the bot reacts to me...
slim skiff
what does it mean when the bot reacts to me...
That's just HaikuBot. It reacts to accidental haikus.
royal dawn
oh
slim skiff
the integral of e^5x is exactly what the question was
I meant, "notice how the derivative of 1/5 is 0?" So the integral of (1/5)e^(5x) is just 1/5 times the integral of e^(5x). Demonstrating that constant multiples don't factor into integrals. In fact, it's common practice to factor constant multiples all the way out to the left of the integral symbol.