Exponential integral: something is wrong.

It seems like a substitution error. Although (1) is equal to (2), when you replace t with u in the first line of the last derivation, u=-t so they are not equal. This results in an false statement when you try to set the end products equal to each other because the variables are used inconsistently.

Topology: reference for "Great Wheel of Compactness"

If $R[x]$ and $R[[x]]$ are isomorphic, then are they isomorphic to $R$ as well? [duplicate]

Suppose $f$ is continuous on $[0,2]$ and $f(0) = f(2)$. For which $a\in(0,2)$ must there exist $x,y\in[0,2]$ so that $|y − x| = a$ and $f(x) = f(y)$?

Geometric intuition of graph Laplacian matrices

Motivation/Intuition behind Lorentz spaces

Probability that an exam will have a perfect predictor

integral $\int_0^{\pi} \left( \frac{\pi}{2} - x \right) \frac{\tan x}{x} \, {\rm d}x$

Multiple of real numbers with only $0$'s and $1$'s in the integer part

Prob. 5, Sec. 20, in Munkres' TOPOLOGY, 2nd ed: What is the closure of $\mathbb{R}^\infty$ in $\mathbb{R}^\omega$ in the uniform topology?

Why do the squared permanents sum to 1?

Find shortest vectors $u_1,v_1,\cdots,u_N,v_N$ such that $\langle u_i,v_j\rangle=1$ if $i\le j$ and $\langle u_i,v_j\rangle=0$ if $i>j$

Divide a square into rectangles where each occurs once in each orientation