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How to use it?
- Integral of d{x}:
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Integral of cosx
- Integral of ln|x|
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Integral of x*sin(x)^2
- Integral of x^n*e^(-x)
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Identical expressions
- x^n*e^(-x)
- x to the power of n multiply by e to the power of ( minus x)
- xn*e(-x)
- xn*e-x
- x^ne^(-x)
- xne(-x)
- xne-x
- x^ne^-x
- x^n*e^(-x)dx
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Similar expressions
- x^n*e^(x)
Integral of x^n*e^(-x) dx
The solution
You have entered
[src]
1 / | | n -x | x *E dx | / 0
$$\int\limits_{0}^{1} e^{- x} x^{n}\, dx$$
Integral(x^n*E^(-x), (x, 0, 1))
Detail solution
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Add the constant of integration:
UpperGammaRule(a=-1, e=n, context=E**(-x)*x**n, symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | | n -x | x *E dx = C - Gamma(1 + n, x) | /
$$\int e^{- x} x^{n}\, dx = C - \Gamma\left(n + 1, x\right)$$
The answer
[src]
Gamma(1 + n)*lowergamma(1 + n, 1) n*Gamma(1 + n)*lowergamma(1 + n, 1)
--------------------------------- + -----------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Gamma\left(n + 1\right) \gamma\left(n + 1, 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Gamma\left(n + 1\right) \gamma\left(n + 1, 1\right)}{\Gamma\left(n + 2\right)}$$
=
=
Gamma(1 + n)*lowergamma(1 + n, 1) n*Gamma(1 + n)*lowergamma(1 + n, 1)
--------------------------------- + -----------------------------------
Gamma(2 + n) Gamma(2 + n)
$$\frac{n \Gamma\left(n + 1\right) \gamma\left(n + 1, 1\right)}{\Gamma\left(n + 2\right)} + \frac{\Gamma\left(n + 1\right) \gamma\left(n + 1, 1\right)}{\Gamma\left(n + 2\right)}$$
gamma(1 + n)*lowergamma(1 + n, 1)/gamma(2 + n) + n*gamma(1 + n)*lowergamma(1 + n, 1)/gamma(2 + n)
Use the examples entering the upper and lower limits of integration.