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Q: If ∫x 3 (√ ((1+x 2 )/(1-x 2 )))dx= A √(1-x 4 ) - Bx 2 (√(1-x 4 ) + C sin -1 (x 2 ) + D ,then A+B+C=?

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

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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