Integral Bessel recurrence relation I want to show that $\int x^vJ_{v-1}(x)dx = x^vJ_v(x) + C$. Now I know the recurrence relations of the Bessel equation/function and the one I need to use is $x^vJ_v(x) = x^vJ_{v-1}(x)$ I'm just thinking to set v as a constant and just integrate with respect to x but the $J_v(x)$ is confusing me...I don't see how that will turn out to be $J_{v-1}(x)$

The relation to use is \begin{align} \frac{d}{dx} \left[ x^{\
u} J_{\
u}(x) \right] = x^{\
u} J_{\
u-1}(x). \end{align} Integrating both sides with respect to $x$ yields \begin{align} \int \frac{d}{dx} \left[ x^{\
u} J_{\
u}(x) \right] \ dx &= \int x^{\
u} J_{\
u-1}(x) \ dx \end{align} or \begin{align} \int x^{\
u} J_{\
u-1}(x) = x^{\
u} J_{\
u}(x) + \mbox{ constant }. \end{align} which provides the desired result.