Question
∫etan−1x(1+x2)[(sec−1√1+x2)2+cos−1(1−x21+x2)]dx(x>0)
Answer: Option C
:
C
note that sec−1√1+x2=tan−1x;cos−1(1−x21+x2)=2tan−1x for x > 0
I=∫etan−1x1+x2((tan−1x)2+2tan−1x)dx
Put tan−1x=t
=∫et(t2+2t)dt=et.t2=etan−1x((tan−1x)2)+C
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:
C
note that sec−1√1+x2=tan−1x;cos−1(1−x21+x2)=2tan−1x for x > 0
I=∫etan−1x1+x2((tan−1x)2+2tan−1x)dx
Put tan−1x=t
=∫et(t2+2t)dt=et.t2=etan−1x((tan−1x)2)+C
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