(adsbygoogle = window.adsbygoogle || []).push({}); Prove two integral identities???

1. The following integral identity holds

[tex]\dfrac{d}{dx}\intop_{x}^{a}\dfrac{F(\rho)d\rho}{\sqrt{\rho^{2}-x^{2}}}=-\dfrac{F(a)x}{a\sqrt{a^{2}-x^{2}}}+x\intop_{x}^{a}\dfrac{d\rho}{\sqrt{\rho^{2}-x^{2}}}\dfrac{d}{d\rho}\left[\dfrac{F(\rho)}{\rho}\right][/tex]

Hints: this can easily proved by applying ingtegration by parts to the right hand side of the identity

2. But the following can also hold

[tex]\dfrac{d}{dx}\intop_{x}^{a}\dfrac{F(\rho)d\rho}{\sqrt{\rho^{2}-x^{2}}}=-\dfrac{F(a)a}{x\sqrt{a^{2}-x^{2}}}+\dfrac{1}{x}\intop_{x}^{a}\dfrac{\rho d\rho}{\sqrt{\rho^{2}-x^{2}}}\dfrac{d}{d\rho}F(\rho)[/tex]

I can not figure out the second identity.Is there anybody can help me?I'm waiting for your excellent proof!!

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# Prove two integral identities?

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