Let $p(x)$ be fifth degree polynomial such that $p(x)+1$ is divisible by $(x-1)^3$ and $p(x)-1 $is divisible by $(x+1)^3 $. Then find the value of the definite integral $$\int _{-10}^{10}p(x)dx$$
Attempt:
$p(x)-1 = (x+1)^3 Q(x)$
$p(x)+1 = (x-1)^3 H(x)$
Where $Q(x)$ and $H(x)$ are unknow...2
In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive.
== Definition ==
For any complex number
τ
{\displaystyle \tau }
with
I
m
(
τ
)
>
0
{\displaystyle Im(\tau )>0}
, let
q
=
e
2
π
i
τ
...
