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Question

Integrate the rational function 1(ex1)

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Solution

1(ex1)
Let ex=texdx=dt
1ex1dx=1t1×dtt=1t(t1)dt
Let 1t(t1)=At+Bt1
1=A(t1)+Bt ............ (1)
Substituting t=1 and t=0 in equation (1), we obtain
A=1 and B=1
1t(t1)=1t+1t1
1t(t1)dt=logt1t+C
=logex1ex+C

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