Question: Does anyone know a book that might help me in Integration?

I want to learn about advanced integration, such as integrating$$\int\limits_{0}^{\infty}\dfrac {\left|\Gamma\left(a+xi\right)\right|^2}{\left|\Gamma\left(b+xi\right)\right|^2}\,dx=\sqrt\pi\dfrac {\Gamma(a)\Gamma\left(a+\frac 12\right)\Gamma\left(b-a-\frac 12\right)}{\Gamma\left(b-\frac 12\right)\Gamma(b)\Gamma(b-a)}$$$$\int\limits_0^\infty\dfrac {1+\frac {x^2}{(b+1)^2}}{1+\frac {x^2}{a^2}}\dfrac {1+\frac {x^2}{(b+1)^2}}{1+\frac {x^2}{(a+1)^2}}\cdots\,dx=\dfrac {\sqrt\pi}{2}\dfrac {\Gamma\left(a+\frac 12\right)\Gamma(b+1)\Gamma\left(b-a+\frac 12\right)}{\Gamma(a)\Gamma\left(b+\frac 12\right)\Gamma(b-a+1)}$$ But I just don't know what book/type of book to look for. I have already learned the basics of integration.

• Commented Feb 5, 2017 at 5:43
• aren't these two integrals almost equivalent? Commented Feb 5, 2017 at 9:11
• books of theoretical/mathematical physics are often a great source of interesting integrals. for example morse/feshbach and courant/hilbert Commented Feb 5, 2017 at 9:12
• @tired Eh... They are very similar to each other. Commented Feb 5, 2017 at 15:06
• @AhmedS.Attaalla That PDF is good, except for the fact that I know nothing about partial derivatives. Know where I can learn them? (I'm teaching myself all of this) Commented Feb 5, 2017 at 17:08