1/4e^-.25x dx

Question

∫1/4e^-.25x dx

Answer 1

We can take out the constants in front of the integral. 

 

(1/4) ∫e^-(1/4)x dx

 

 

We can use the u substitution method to solve this integral.

 

Let u = (-1/4)x

 

Let du = (-1/4)dx  --->  dx = -4du

 

 

Rewrite the integral using the substitution.

 

-4(1/4) ∫e^u du =

 

-∫e^u du

 

 

We know the derivative of e^x is the function itself.  So the integral of e^x is the function itself.

 

-e^u  + C

 

 

Substitute u back into the term of x.

 

-e^(-1/4)x + C

Answer 2

∫(1/4)e^-.25x dx = (1/4)∫e^-x/4 dx

 

Use the substitution u = -x/4

• du = -1/4 dx
• So -4du = dx

 

-(1/4)∫4e^u du = -e^u + C = -e^-x/4 + C

 

where C is a constant of integration.