What's happening at $a=-1$ in $\int x^a dx$?
12217
What is so special about $\alpha=-1$ in the integral of $x^\alpha$?
14161
Proof of when is $A=X^TX$ invertible?
60900
If $A^2=-I$, Prove that $\det{A}=1$
118314
How to define $x^a$ for arbitrary real numbers $x$ and $a$
116043
Why is a raised to the power of Zero is 1?
5180
How to show $\alpha\int_a^cf(x)dx+\beta \int_c^b f(x)dx =0$ means $f(x)=0$ everywhere $?$
107390
Why is (-1)(-1) = 1?
126654
What is the definite integral $\int_{-1}^1 \frac{1}{x} dx$ equal to?
53518
Integrating : $\int_0^1 {\frac {x^a-x^b} {\ln x} dx}$
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
47793
Integral $\int_0^1\sqrt{1-x^4}dx$
27482
How to show $-\sup(-A)=\inf(A)$?
149576
$x(a^{1/x}-1)$ is decreasing
40047
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
81875
why is $\sqrt{-1} = i$ and not $\pm i$?
101169
Prove that $x^2 = - 1$ has no solution in $\mathbb{Z}$
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?