\Rightarrow dr=\lambda dx$, $r=\lambda x$
$\Rightarrow
I_c=j_c(R)2\pi \lambda^2 \exp(-R/\lambda) \int_0^R d(\frac{r}{\lambda})
- \, \frac{r}{\lambda} \exp(\frac{r}{\lambda})$
+ \, \frac{r}{\lambda} \exp(\frac{r}{\lambda})$\\
Integration by parts: $\int uv' = uv - \int vu'$\\
$\int xe^x dx = xe^x-\int e^x dx=xe^x-e^x+c=e^x(x-1)+c$\\
$\Rightarrow