Question

solve this integration

Answer 1

Step 1: Cut off the unnecessary .
Step 2: Now the integrand is 1/(eˣ - 1)
Step 3: Modify the numerator into eˣ - 1 - eˣ
Step 4: Separate into two parts, which gives 1 -  {eˣ/(eˣ - 1)}
Step 5: Separate the integration for these 2 parts. 
Integrate 1 to give x. Now, integrate the 2nd part.
Step 6: To integrate the 2nd part: 
                                                          Take eˣ - 1 = z                        
                                                            ⇒ eˣdx = dz        
 We already have eˣdx in the numerator, so replace it with dz and replace the denominator with z. Integrate that to give log |z|, which is actually log |eˣ - 1|

So, your final answer becomes x - log |eˣ - 1| + C.
NOTE: THE LOGARITHM USED HERE HAS "e" AS ITS BASE.

Answer 2

Answer:

Step-by-step explanation:

let e^x=t

e^x dx =dt

∫dt/t(t-1)

∫-1/t+1/t-1

-log t +log t-1

log t-1 /t

log e^x-1 /e^x