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- Improper integral
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- Curvilinear integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(x^2+3)
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Integral of x*e^(x^2)
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Integral of xexp(-x)
- Integral of xtanx
- Sum of series:
- nx^(n-1)
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Identical expressions
- nx^(n- one)
- nx to the power of (n minus 1)
- nx to the power of (n minus one)
- nx(n-1)
- nxn-1
- nx^n-1
- nx^(n-1)dx
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Similar expressions
- nx^(n+1)
Integral of nx^(n-1) dx
The solution
You have entered
[src]
1 / | | n - 1 | n*x dx | / 0
$$\int\limits_{0}^{1} n x^{n - 1}\, dx$$
Integral(n*x^(n - 1), (x, 0, 1))
Detail solution
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The integral of a constant times a function is the constant times the integral of the function:
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The integral of is when :
So, the result is:
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Now simplify:
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Add the constant of integration:
The answer is:
The answer (Indefinite)
[src]
/ // n \
| || x |
| n - 1 || -- for n - 1 != -1|
| n*x dx = C + n*|< n |
| || |
/ ||log(x) otherwise |
\\ /
$$\int n x^{n - 1}\, dx = C + n \left(\begin{cases} \frac{x^{n}}{n} & \text{for}\: n - 1 \neq -1 \\\log{\left(x \right)} & \text{otherwise} \end{cases}\right)$$
The answer
[src]
/ n | 1 - 0 for And(n > -oo, n < oo, n != 0) < |oo*sign(n) otherwise \
$$\begin{cases} 1 - 0^{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\infty \operatorname{sign}{\left(n \right)} & \text{otherwise} \end{cases}$$
=
=
/ n | 1 - 0 for And(n > -oo, n < oo, n != 0) < |oo*sign(n) otherwise \
$$\begin{cases} 1 - 0^{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\infty \operatorname{sign}{\left(n \right)} & \text{otherwise} \end{cases}$$
Piecewise((1 - 0^n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (oo*sign(n), True))
Use the examples entering the upper and lower limits of integration.