| Summary: | The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mo>∫</mo> <mrow> <mn>0</mn> </mrow> <mo>∞</mo> </msubsup> <mo form="prefix">log</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>±</mo> <msup> <mi>e</mi> <mrow> <mo>−</mo> <mi>α</mi> <mi>y</mi> </mrow> </msup> <mo>)</mo> </mrow> <mi>R</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>y</mi> </mrow> </semantics> </math> </inline-formula> in terms of a special function, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> is a general function and <i>k</i>, <i>a</i> and <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> are arbitrary complex numbers, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>(</mo> <mi>α</mi> <mo>)</mo> <mo>></mo> <mn>0</mn> </mrow> </semantics> </math> </inline-formula>.
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