$\Rightarrow$
$n=\frac{1}{2\pi^2}(\frac{2m_nk_{\text{B}}T}{\hbar^2})^{3/2}
\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})
$\Rightarrow$
$n=\frac{1}{2\pi^2}(\frac{2m_nk_{\text{B}}T}{\hbar^2})^{3/2}
\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})
\underbrace{2(\frac{m_nk_{\text{B}}T}{2\pi\hbar^2})^{3/2}}_{=N_{\text{c}}}
\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})=
N_{\text{c}}\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})$
\underbrace{2(\frac{m_nk_{\text{B}}T}{2\pi\hbar^2})^{3/2}}_{=N_{\text{c}}}
\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})=
N_{\text{c}}\exp(-\frac{E_{\text{c}}-\mu_{\text{F}}}{k_{\text{B}}T})$
\exp(\frac{\epsilon-\mu_{\text{F}}}{k_{\text{B}}T})$\\
Parabolic approximation:
$D_v(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}(E_v-\epsilon)^{1/2}$
\exp(\frac{\epsilon-\mu_{\text{F}}}{k_{\text{B}}T})$\\
Parabolic approximation:
$D_v(\epsilon)=\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}(E_v-\epsilon)^{1/2}$
\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}
\exp(-\frac{\mu_{\text{F}}}{k_{\text{B}}T})
\int_{-\infty}^{E_{\text{v}}}(E_v-\epsilon)^{1/2}
\frac{1}{2\pi^2}(\frac{2m_p}{\hbar^2})^{3/2}
\exp(-\frac{\mu_{\text{F}}}{k_{\text{B}}T})
\int_{-\infty}^{E_{\text{v}}}(E_v-\epsilon)^{1/2}
$\Rightarrow$
$p=\frac{1}{2\pi^2}(\frac{2m_pk_{\text{B}}T}{\hbar^2})^{3/2}
\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})
$\Rightarrow$
$p=\frac{1}{2\pi^2}(\frac{2m_pk_{\text{B}}T}{\hbar^2})^{3/2}
\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})
\underbrace{2(\frac{m_pk_{\text{B}}T}{2\pi\hbar^2})^{3/2}}_{=N_{\text{v}}}
\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})=
N_{\text{v}}\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})$
\underbrace{2(\frac{m_pk_{\text{B}}T}{2\pi\hbar^2})^{3/2}}_{=N_{\text{v}}}
\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})=
N_{\text{v}}\exp(\frac{E_{\text{v}}-\mu_{\text{F}}}{k_{\text{B}}T})$