The problems in this section are concerned with the method of integration by par

Question

The problems in this section are concerned with the method of integration by parts which is simply the following

Here we have written the functional as opposed to differential form found in the book

The problems in this section are concerned with the method of integration by parts which is simply the following displaystyle v = ___________ (C) Evaluate the integral ______________________________ + C dx and displaystyle dv = ________ dx (B) Find displaystyle du = __________ displaystyle u = _________ and int x^2 ln(x) , dx (A) Find v = g(x) . In this exercise we want to use integration by parts to integrate du = f'(x) dx and int u , dv =uv - int v , du so int f'(x)g(x) , dx = f(x)g(x) - int f(x)g'(x) , dx Here we have written the functional as opposed to differential form found in the book

Explanation / Answer

Solution:

Part-a

let u = ln(x) ;

du = dx / x

Part-b:
dv = x

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