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Question

Solve: dx214xx2

A
arcsin(x+4)5+C
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B
arcsin(x+2)5+C
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C
arcsin(x4)5+C
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D
None of these
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Solution

The correct option is B arcsin(x+2)5+C
Let I=dx214xx2
cscucotu du=cscu+C
dua2u2=arcsin ua+C
dua2+u2=1aarctan ua+C
duuu2a2=1aarcsecua+C
duu2a2=12alnuau+a+C
dua2u2=12alna+uau+C
Taking only the denominator part, split 21 as 254
Now this 4 goes with the other terms to make another term u2, where u=x+2.
I=dx52(x+2)2=arcsin (x+2)5+C

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