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Question

If I=xx2+1x21dx, then I equals

A
12x41+12x4+1+C
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B
12x41+12log(x2+x41)+C
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C
x41+sin1(x2)+C
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D
x41+2sin1(x2)+C
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Solution

The correct option is B 12x41+12log(x2+x41)+C
Let I=xx2+1x21dx
Substitute x2=t2xdx=2t
I=12t+1t1dt=12t+1t21dt
=12tt21dt+12dtt21
=12t21+12logt+t21+C
=12x41+12logx2+x41+C

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