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Evaluate the definite integral (X^4)/(1-X^4) Cos^(-1)[2x/(1+x^2)] limit [-1/root3, 1/root3]

Evaluate the definite integral (X^4)/(1-X^4) Cos^(-1)[2x/(1+x^2)]  limit [-1/root3, 1/root3]

Grade:12th pass

1 Answers

Aditya Gupta
2075 Points
2 years ago
Assume the function to be integrated f(x)
Now replace the function by f(a+b-x) or f(-x) in this case and then add both eqns. 
But arccosy+arccos(-y)=π
So 2I/π= integral of x^4/(1-x^4)
Now write it as 1/(1-x^4) - 1
Use partial fractions for 1/(1-x^4) and the question Will be solved

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