Question

I'm trying to do an integral by u-substitution that I can't figure out. I've done to Wolfram|Alpha and I literally just don't understand the steps it's taking, would really appreciate help.

Answer 1

Since I can't use the LaTeX editor, the integrand is 1/(e^z +1)dz. Again, supposed to use u-substitution.

Answer 2

The way that W|A is approaching it, they are taking e^z to be u, and e^z dz to be du, which makes perfect sense. What I don't understand, however, is what they're doing in the denominator. After stating that substitution, the denominator was somehow factored to u(u+1). How can this be? e^z + 1 =/= e^2z + e^z, which is what u(u+1) would be if expanded with the non-substituted values, yes?

Answer 3

@ganeshie8 This one is a little different, help would be very much appreciated if you get the chance.

Answer 4

hint : 1/(e^z + 1) = e^z/[e^z(e^z+1)]

Answer 5

just multiply both numerator and denominator wid e^z

Answer 6

Ah! So they're just including the e^z from the derivative of the original u-sub into the du?

Answer 7

yup !

Answer 8

Thanks!

Answer 9

np :)