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Question

If ln403e4x+2e3x+e2x4e4x+e3x+e2x+ex+4dx=ln(a4), where aR, then the value of a is

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Solution

I=ln403e4x+2e3x+e2x4e4x+e3x+e2x+ex+4dxI=ln40[4e4x+3e3x+2e2x+exe4x+e3x+e2x+ex+4e4x+e3x+e2x+ex+4e4x+e3x+e2x+ex+4]dx
I=ln40[4e4x+3e3x+2e2x+exe4x+e3x+e2x+ex+41]dx
I=[ln(e4x+e3x+e2x+ex+4)x]ln40I=ln(44+43+42+41+4)ln(8)ln(4)I=ln(434)a=43

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