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Question

Solve: x21(x4+3x2+1)tan1(x+1x)dx

A
=lntan1(x+1x)+C
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B
=tan1(x+1x)+C
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C
=tan1(x+1x)+C
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D
=lntan1(x1x)+C
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Solution

The correct option is A =lntan1(x+1x)+C
I=x21(x4+3x2+1)tan1(x+1x)dx

=x2(11x2)x2(x2+1x2+3)tan1(x+1x)dx

=11x2(x2+1x2+3)tan1(x+1x)dx

Substitute x+1x=t or (11x2)dx=dt and x2+1x2+2=t2

I=dt(t2+1)tan1t=lntan1t+C [f(x)f(x)dx=log|f(x)|+C]

=lntan1(x+1x)+C

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