∫ex1+ex2+exdx is equal to 

ex1+ex2+exdx is equal to 

  1. A

    log2+ex1+ex+C

  2. B

    log1+ex1ex+C

  3. C

    12log2+ex1+ex+C

  4. D

    log1+ex2+ex+C

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    Solution:

    Let,I=ex1+ex2+exdx

    put,ex=texdx=dt

     I=ex(1+t)(2+t)dtex=1(1+t)(2+t)dt Let 1(1+t)(2+t)=A(1+t)+B(2+t) 1=A(2+t)+B(1+t)=(2A+B)+t(A+B)

    On equating the coefficients of t and constant term on
    both sides, we get A+B=0 and 2A+B=1

     On solving both equations, we get A=1 and B=1

     I=1(1+t)dt1(2+t)dt=log|1+t|log|2+t|+C=log1+t2+t+C=log1+ex2+ex+C

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