Evaluate the integral

Calculus
Tutor: None Selected Time limit: 1 Day

Aug 3rd, 2015

Thank you for the opportunity to help you with your question!

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


Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 3rd, 2015

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

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



Aug 3rd, 2015

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