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Question

x3/2+x5/2+xx2+2x1/2+x+1dx equals

A
23x3/2+xtan1x1/4+C
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B
23x5/2x+tan1x1/2+C
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C
23x1/2xtan1x1/4+C
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D
23x3/2x+tan1x1/4+C
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Solution

The correct option is A 23x3/2+xtan1x1/4+C
Let I=x3/2+x5/2+xx2+2x1/2+x+1=x(x1/2+x3/2+1)x2+x1/2+x+x1/2+1+x3/2

=x(x1/2+x3/2+1)x1/2(x3/2+x1/2+1)+1(x3/2+x1/2+1)

=x(x3/2+x1/2+1)(x1/2+1)(x3/2+x1/2+1)=x1+1x+1

=(x)2(1)2x+1+1x+1=(x1)+1(x+1)

Idx=((x1)+1(x+1))dx

=(x1)dx+1x+1dx

=x3/23/2x+1(x1/4)2+(1)2dx=23x3/2+xtan1x1/4+C

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