To integrate e^ax, also written as ∫e ax dx, we notice that it is an exponential and one of the easiest in calculus to perform. As you can see, the general rule is very simple, and worth remembering.
Apr 21, 2023 · In mathematical form, the integral of e^ax is: ∫ e a x d x = e a x a + c. Where c is any constant involved, dx is the coefficient of integration and ∫ is the symbol of the integral. Use our integration calculator to evaluate the integration of e^ …
For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative functions. A constant (the constant of integration) may be added to the right hand side of any of these formulas, but has been suppressed here in the interest of brevity.
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∫ a e − ax dx = 1 . Notice the minus sign in the exponent: we need an integrand that decreases as x goes towards infinity, otherwise the integral will itself be infinite. To visualize this result, we plot below e-x and e-3x.