10 / | | d*x | --------- dx | _______ | \/ x - 1 | / 5
Integral((d*x)/sqrt(x - 1), (x, 5, 10))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Integrate term-by-term:
The integral of is when :
The integral of a constant is the constant times the variable of integration:
The result is:
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | / 3/2\ | d*x | _______ (x - 1) | | --------- dx = C + 2*d*|\/ x - 1 + ----------| | _______ \ 3 / | \/ x - 1 | /
Use the examples entering the upper and lower limits of integration.