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Question

Integrate with respect to x:
1x2+2x+5

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Solution

Given: dxx2+2x+5

=dxx2+2x+11+5

=dx(x+1)2+4

=dx(x+1)2+22

=12tan1(x+21)+c

[dxx2+a2=1atan1(xa)+c]

dxx2+2x+5=12tan1(x+21)+c

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