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Question

Integrate following with respect to x.
(i) x2+4 (ii) x2+2x+5

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Solution

(i) x2+4dx

=x2+22dx

=x2x2+4+42sin1(x2)+C..........[x2+a2dx=x2x2+a2+a22sin1(xa)+C]

x2+4dx=x2x2+4+2sin1(x2)+C


(ii) x2+2x+5dx

=(x+1)2+22 dx

=(x+2)2x2+2x+5+42sin1(x+12)+C

x2+2x+5dx=(x+12)x2+2x+5+2sin1(x+12)+C

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