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this integral can be solved

S e^-4x(5+e^-2x) dx

S5e^(-4x)+ e^-4x *e^-2x dx

=-e^-6x(15e^2x+2)/15 +C

sorry due to time limit i cannot solve it properly

we can solve this by substitution

e^-2x=v

dv/dx=-e^(-2x)/2

dv =e^(-2x)/2 dx

so the integral becomes

S 5e^(-2x)^2dx+ e^-2x e^-4xdx

S -10vdv-2v^2dv

-10v^2/2 -2v^3/3 +C

-5v^2 -2/3 v^3 +C

-5e^-4x -2/3 e^-6x +C is the solution of the integral

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