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Q.

∫dxx2x4+13/4=Ax4+1x4B+C

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a

A=−1,B=14

b

A=1,B=−14

c

A=12,B=1

d

A=−12,B=−1

answer is A.

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Detailed Solution

I=∫dxx2x4+13/4=∫dxx2⋅x31+1x43/4Put⁡1+x−4=t⇒−4x5dx=dt⇒−14∫dtt3/4=14∫t−3/4dt=−14⋅t1/41/4+C=−1+1x41/4+C=−1+x4x41/4+C Hence,  A=−1,B=14
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