Divergent Integrals

SUBSECTIONS

Exponential Integrals

$\displaystyle \int_1^{\infty_+} a^t \, dt = \dfrac{1-a}{\ln a} \qquad (a>1)$

$\displaystyle \int_1^{\infty_+} e^{at} \, dt = \dfrac{1-e^a}{a}$

$\displaystyle \int_1^{\infty_+} e^{iat} \, dt = i \, \dfrac{e^{ia}-1}{a} = -\dfrac{\sin a}{a} \,+\, i \, \dfrac{\cos a - 1}{a}$

Trigonometric Integrals

$\displaystyle \int_1^{\infty_+} \sin(at) \, dt = \dfrac{\cos a - 1}{a}$

$\displaystyle \int_1^{\infty_+} \cos(at) \, dt = -\dfrac{\sin a}{a}$

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