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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of (x+1)e^(2x)
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Integral of (x+1)/(2x²+3x-4)
- Integral of e^(3/x)
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Integral of dx/(3*x-2)
- Derivative of:
- exp(-a*x)
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Identical expressions
- exp(-a*x)
- exponent of ( minus a multiply by x)
- exp(-ax)
- exp-ax
- exp(-a*x)dx
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Similar expressions
- x*exp(-ax)*dx
- x^2*exp(-a*x^2)
- exp(a*x)
- a*exp^(-ax)dx
Integral of exp(-a*x) dx
The solution
You have entered
[src]
oo / | | -a*x | e dx | / -oo
$$\int\limits_{-\infty}^{\infty} e^{- a x}\, dx$$
Integral(exp((-a)*x), (x, -oo, oo))
The answer (Indefinite)
[src]
/ // -a*x \
| ||-e |
| -a*x ||------- for a != 0|
| e dx = C + |< a |
| || |
/ || x otherwise |
\\ /
$$\int e^{- a x}\, dx = C + \begin{cases} - \frac{e^{- a x}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}$$
The answer
[src]
/ / pi pi\ | 0 for And||pi + arg(a)| < --, |arg(a)| < --| | \ 2 2 / | | oo | / < | | | -a*x | | e dx otherwise | | |/ |-oo \
$$\begin{cases} 0 & \text{for}\: \left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2} \wedge \left|{\arg{\left(a \right)}}\right| < \frac{\pi}{2} \\\int\limits_{-\infty}^{\infty} e^{- a x}\, dx & \text{otherwise} \end{cases}$$
=
=
/ / pi pi\ | 0 for And||pi + arg(a)| < --, |arg(a)| < --| | \ 2 2 / | | oo | / < | | | -a*x | | e dx otherwise | | |/ |-oo \
$$\begin{cases} 0 & \text{for}\: \left|{\arg{\left(a \right)} + \pi}\right| < \frac{\pi}{2} \wedge \left|{\arg{\left(a \right)}}\right| < \frac{\pi}{2} \\\int\limits_{-\infty}^{\infty} e^{- a x}\, dx & \text{otherwise} \end{cases}$$
Piecewise((0, (Abs(arg(a)) < pi/2)∧(Abs(pi + arg(a)) < pi/2)), (Integral(exp(-a*x), (x, -oo, oo)), True))
Use the examples entering the upper and lower limits of integration.