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Question:

Evaluate: ∫-22x2/(1+5x)dx

Solution:

Let
I=∫-22x2/(1+5x)
we know that
∫abf(x)=∫abf(a+b-x)
Therefore
I=∫-22x2/(1+5x)
and
I=∫-22(-x)2/(1+5-x)=∫-22x25x/(1+5x)
Add above two , we get
2I=∫-22x25x/(1+5x)+∫-22x2/(1+5x)=∫-22x2=(2)3/3-(-2)3/3=16/3
Therefore
I=8/3