Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 15/Definite Integrals involving Exponential Functions

Definite Integrals involving Exponential Functions

$15.68$: Definite Integral to Infinity of $e^{-a x} \cos b x$

$15.69$: Definite Integral to Infinity of $e^{-a x} \sin b x$

$15.70$: Definite Integral to Infinity of $\dfrac {e^{-a x} \sin b x} x$

$15.71$: Definite Integral to Infinity of $\dfrac {e^{-a x} - e^{-b x} } x$

$15.72$: Definite Integral to Infinity of $e^{-a x^2}$

$15.73$: Definite Integral to Infinity of $e^{-a x^2} \cos b x$

$15.74$: Definite Integral to Infinity of $\map \exp {-\paren {a x^2 + b x + c} }$

$15.75$: Definite Integral over Reals of $\map \exp {-\paren {a x^2 + b x + c} }$

$15.76$: Definite Integral to Infinity of $x^n e^{-a x}$

$15.77$: Definite Integral to Infinity of $x^m e^{-a x^2}$

$15.78$: Definite Integral to Infinity of $\map \exp {a x^2 + \dfrac b {x^2} }$

$15.79$: Definite Integral to Infinity of $\dfrac x {e^x - 1}$

$15.80$: Definite Integral to Infinity of $\dfrac {x^{n - 1} } {e^x - 1}$

$15.81$: Definite Integral to Infinity of $\dfrac x {e^x + 1}$

$15.82$: Definite Integral to Infinity of $\dfrac {x^{n - 1} } {e^x + 1}$

$15.83$: Definite Integral to Infinity of $\dfrac {\sin m x} {e^{2 \pi x} - 1}$

$15.84$: Definite Integral to Infinity of $\paren {\dfrac 1 {1 + x} - e^{-x} } \dfrac 1 x$

$15.85$: Definite Integral to Infinity of $\dfrac {e^{-x^2} - e^{-x} } x$

$15.86$: Definite Integral to Infinity of $\dfrac 1 {e^x - 1} - \dfrac {e^{-x} } x$

$15.87$: Definite Integral to Infinity of $\dfrac {e^{-a x} - e^{-b x} } {x \sec p x}$

$15.88$: Definite Integral to Infinity of $\dfrac {e^{-a x} - e^{-b x} } {x \csc p x}$

$15.89$: Definite Integral to Infinity of $\dfrac {e^{-a x} \paren {1 - \cos x} } {x^2}$