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see attachment and explain it

 see attachment and explain it

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Grade:12

1 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
f(x) = (x^2 + 1) / (x^4 +1)
divided num & den by x^2
f(x) = (1 + 1/x^2 ) / (x^2 + 1/x^2)
put x – 1/x = t = > 1 + 1/x^2 dx = dt  
& x^2 + 1/x^2 = (x – 1/x)^2 + 2 = t^2 + 2
∫(x^2 + 1) / (x^4 +1) dx = ∫ dt / t^2 + 2 = 1/sqroot (2) * tan ^-1( t/sqroot (2))
= [1/sqroot (2) ]* tan ^–1 [(x^2 – 1)/(x * sqroot (2))] + c
 
 
 
 
 

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