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I was wondering if anyone can suggest a textbook that encapsulates a fairly large range of evaluating integrals. I find this particular subject quite intriguing and what to expand my knowledge of it .

Hence, I'm mainly interested in topics such :

$\bullet$ Complex integration

$\bullet$ More advanced techniques on multivariable real functions

$\bullet$ Parametric integration

$\bullet$ Methods involving power series and generating functions

$\bullet$ Special functions (such as $\Gamma , \beta , \digamma$ etc.)

$\bullet$ Substitutions

$\bullet$ Use of transforms in integration ( Mellin, Laplace, Fourier, etc.)

Surely I've only managed to list a fraction of the integration techniques known nowadays, but those are my current tools in the area. I don't know if the topics I've mentioned might be too disconnected to be covered in one textbook, but I'm basically a beginner in this area, so feel free to suggest whatever you have in mind.

I should emphasize that the focus of the suggested textbook must be integration methods . Also, there should be a fair number of problems to solve.

Thank you.

Victor
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    This question has couple of excellent answers listing what are probably the best resources we currently have on integration, unless you start digging into specialist resources like Watson's Bessel Functions treatise, or looking at chunks of Gradshteyn and Ryzhik. – Chappers Sep 24 '15 at 20:10

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You might try $\mathbf{The \, Handbook \, of \, Integration}$ by Dan Zwilliger. It is not really a textbook, but it hits lots of techniques and gives references if you want to dig deeper into a particular topic. The Amazon page for the book lets you look inside.

Math Prof
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