Question Number 215185 by MrGaster last updated on 31/Dec/24
$$\int_{−\infty} ^{\infty} \frac{\mathrm{exp}\left(\frac{{ax}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\mathrm{exp}\left(\frac{{a}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx},{a}>\mathrm{0} \\ $$
Answered by MathematicalUser2357 last updated on 31/Dec/24
$$\mathrm{Oops}!\:\mathrm{Make}\:\mathrm{sure}\:\mathrm{you}\:\mathrm{typed}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{made}\:\mathrm{of}\:{x}. \\ $$
Answered by JamesZhou last updated on 01/Jan/25
Commented by MathematicalUser2357 last updated on 04/Jan/25
$$\Rightarrow\:\pi{e}^{\frac{{a}}{\mathrm{2}}} {I}_{\mathrm{0}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{a}\right) \\ $$