Question:
Integral 1-x/1+x dx
Answer:
Given, (1 - x)/(1 + x) = (1 - x + 1 - 1)/(1 + x)
=> (1 - x)/(1 + x) = {2 - (1 + x)}/(1 + x)
=> (1 - x)/(1 + x) = 2/(1 + x) - 1
Now, ∫(1 - x)/(1 + x) dx = ∫{2/(1 + x) - 1} dx
=> ∫(1 - x)/(1 + x) dx = ∫2/(1 + x) dx - ∫dx
=> ∫(1 - x)/(1 + x) dx =2*log(1 + x) - x + C {C is a constant}
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