1 / | | n - 1 | n*x dx | / 0
Integral(n*x^(n - 1), (x, 0, 1))
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ // n \ | || x | | n - 1 || -- for n - 1 != -1| | n*x dx = C + n*|< n | | || | / ||log(x) otherwise | \\ /
/ n | 1 - 0 for And(n > -oo, n < oo, n != 0) < |oo*sign(n) otherwise \
=
/ n | 1 - 0 for And(n > -oo, n < oo, n != 0) < |oo*sign(n) otherwise \
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.