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I want to solve following integral$$\int J_0(x)J_1(x) dx$$I tried so many different ways but I couldn't find a way to attack this problem! please help me

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    $\begingroup$ Think about what is the derivative of $J_0(x)$ $\endgroup$ – Claude Leibovici Mar 8 '17 at 10:25
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Hint: use the substitution $u=J_0(x)$.

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you can find the integral representation of Bessel function here https://en.wikipedia.org/wiki/Bessel_function#Bessel.27s_integrals

That would be helpful.

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