If ∫4ex+6e−x9ex−4e−x dx=Ax+Blog(9e2x−4)+c then 36A+B=

If 4ex+6ex9ex4exdx=Ax+Blog(9e2x4)+c then 36A+B=

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    Solution:

    4ex+6ex9ex4exdx=Ax+Blog(9e2x4)+c

    Differentiate w.r.t x on both sides

    4ex+6ex9ex4ex=A+B9e2x.29e2x-4

    4ex+6ex9ex4ex=9A e2x-4A+18B e2x9.e2x-4

    4ex+6ex9ex4ex=9A ex-4Ae-x+18B ex9.ex-4e-x

     equate e-x coefficients on both sides then 6=-4A

    A=-3/2

     equate ex coefficients on both sides then 4=9A+18B

    4=9-32+18B

    4=-272+18B

    B=3536

    36A+B=36-32+3536=-19

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