Q: If ∫x³(√ ((1+x²)/(1-x²)))dx= A √(1-x⁴) - Bx²(√(1-x⁴) + C sin^-1 (x²) + D ,then A+B+C=?

Dear Tapasranjan

∫x³(√ ((1+x²)/(1-x²)))dx= A √(1-x⁴) - Bx²(√(1-x⁴) + C sin^-1 (x²) + D

differentiate w.r.t x

 and simplify

 x² +x⁴ = x²(-2A) + x⁴(4B) +2C -2B

compair coefficient of same power of x

 -2A =1

  A =-1/2

4B =1

 B=1/4

2C -2B =0

 C=B=1/4

now  A+B+C =0

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