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avatar+55 

evalute the integral ∫ (e^3x + 5e^-x ) dx ?

 May 1, 2020
 #1
avatar+111329 
+1

∫  e3x + 5e-x  dx   =

 

(1/3)e3x  +   (-5)e-x    +  C

 

cool cool cool

 May 1, 2020
 #2
avatar+55 
+1

how can you tell me the steps?

 May 1, 2020
 #3
avatar+111329 
+1

The  best  way to see this is just  to realize the anti-derivative properties of  both functions

 

eax  has  the anti-derivative  of   (1/a) eax

So......letting  a  = 3  we have that

e3x  =  (1/3)e3x  

 

Similarly...lettig a  = -1   we have

5 (e -x)  =  5 ( e -1x)  =  5 ( 1/-1) (e-1x)  =  5 (-1)e-x  =  -5e-x

 

 

cool cool cool

 May 1, 2020

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