Integration by parts | How to choose u and dv

#Integration #by #Parts is a special method of integration that is often useful when two or more functions are multiplied together, most especially different functions.

You will see plenty of examples soon, but first let us see the rule:

if y = uv, where u and v are functions of x.
the derivative of y with respect to x
dy/dx = u(dv/dx) + v(du/dx)
dy = udv + vdu

by taking the integral of each term,
∫dy = ∫udv + ∫vdu
y = ∫udv + ∫vdu

but y = uv

uv = ∫udv + ∫vdu
∫udv = uv - ∫vdu
∫udv = uv − ∫vdu

Guidelines for Selecting u and dv :
(There are always exceptions, but these are generally helpful)
" L - I - A - T - E ” Choose 'u' to be the function that comes first in this list :
L : Logrithmic Function
I : Inverse Trig Function
A : Algebraic Function
T : Trig Function
E : Exponential Function

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[Kdd]

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[TemmyEduConsult]

Weldone sir, pls i need your help on question 2, i got confused when you are doing the second integration by part, why is u = x and not 2x? Thanks as i wait your response.