find the indefinite integral

Question

e^8x/1 + e^8x dx

Answer 1

e^8x/1 + e^8x dx

 

Please check your question e^8x/1 is equivalent to e^8x is the 1 in the denominator correct?

 

So ∫(e^8x)/(1+e^8x)dx

Let u=e^8x then du =8e^8x

then ∫1/8(8e^8x)/(1+e^8x)

so we have 1/8∫1/(1+u)du

1/8 ∫(1+u)^-1du

1/8 ln(1+u)