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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of -lnx
- Integral of ln(x)^n
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Integral of 3^(2x-1)
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Integral of 21x^2
- Sum of series:
- ln(x)^n
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Identical expressions
- ln(x)^n
- ln(x) to the power of n
- ln(x)n
- lnxn
- lnx^n
- ln(x)^ndx
Integral of ln(x)^n dx
The solution
You have entered
[src]
1 / | | n | log (x) dx | / 0
$$\int\limits_{0}^{1} \log{\left(x \right)}^{n}\, dx$$
Integral(log(x)^n, (x, 0, 1))
Detail solution
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Let .
Then let and substitute :
UpperGammaRule(a=1, e=n, context=_u**n*exp(_u), symbol=_u)
Now substitute back in:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ | | n -n n | log (x) dx = C + (-log(x)) *log (x)*Gamma(1 + n, -log(x)) | /
$$\int \log{\left(x \right)}^{n}\, dx = C + \left(- \log{\left(x \right)}\right)^{- n} \log{\left(x \right)}^{n} \Gamma\left(n + 1, - \log{\left(x \right)}\right)$$
The answer
[src]
1 / | | n | log (x) dx | / 0
$$\int\limits_{0}^{1} \log{\left(x \right)}^{n}\, dx$$
=
=
1 / | | n | log (x) dx | / 0
$$\int\limits_{0}^{1} \log{\left(x \right)}^{n}\, dx$$
Integral(log(x)^n, (x, 0, 1))
Use the examples entering the upper and lower limits of integration.