Find the constant term in the expansion of $(x^2+1)(x+\frac{1}{x})^{10}$ I can't solve this problem. How to solve it?
The Problem is 
"Find the constant term in the expansion of $
\left({{x}^{2}\mathrm{{+}}{1}}\right){\left({{x}\mathrm{{+}}\frac{1}{x}}\right)}^{\mathrm{10}}
$"

$f(x)=(x^2+1)(x+\dfrac{1}{x})^{10}$
We can rewrite $f(x)$ like below:
$f(x) = x^2(x+\dfrac{1}{x})^{10} + (x+\dfrac{1}{x})^{10}$
In the first term, the power of $x$, must be $-2$ in the parenthesis, so the when it's multiplyed by $x^2$  the power of $x$ becomes $0$.    And we know that:
$(x+\dfrac{1}{x})^{10}=\sum_{k=0}^{10}\binom{10}{k}x^k(\dfrac{1}{x})^{10-k}$
So $k+k-10=-2=>k=4$. So the coefficient of that term is $\binom{10}{4}$.
On the other hand, the coefficient of the constant term of the second term of $f(x)$ which is just $(x+\dfrac{1}{x})^{10}$, is when $k=5$. So the coefficient would be $\binom{10}{5}$
So the answer is:
$\binom{10}{4}+\binom{10}{5}$
