I mean this is just IBP arranged in a neatly order, bc you always have to choose the same u's and dv's, otherwise you'll end up right where you started.

@TheUnqualifiedTutor

Ай бұрын

Yeah, I appreciate you said that. Should've made it clearer in the video, it is essentially the same. I just like to use little shortcuts. Thanks!

The 1st problem is just extended by parts and second problem uses normal by parts, the DI technique does help the newcomers because it is easier to remember than the by parts formula. With all that said, you gave a great explanation on the technique and hope you keep it up.

@TheUnqualifiedTutor

Ай бұрын

Yeah, pick whichever suits you best! Much love bro.

Well explained

Can you give an example for an exponential function? Say sinx e^x

@Hacker097

Ай бұрын

nvm I got it. Just have to do it twice.

@carultch

Ай бұрын

This one is an example of a looper, where you end up spotting the original integral across a row. In these examples with a simple exponential and either sine or cosine, it is arbitrary which function gets which treatment. Another method is to rewrite sin(x)*e^x, as e raised to a complex exponent, and avoid IBP entirely. Let e^x be integrated, and sin(x) be differentiated. S _ _ _ D _ _ _ _ I + _ _ sin(x) _ _ e^x - _ _ cos(x) _ _ e^x + _ _ -sin(x) _ _ e^x Spot the original integral across bottom row, call it I. Construct result: I = sin(x)*e^x - cos(x)*e^x - I Solve for I algebraically: I = 1/2*e^x * (sin(x) - cos(x)) Add +C, and we're done: 1/2*e^x * (sin(x) - cos(x)) + C

Integrate this wrt r from r=a to r=a/10: 1/√(2μ/r -2μ/a), a is constant>x, μ is constant. Also, 6/10⁷