1 / | | 1 | ------------- dx | ___ | 3*x - 4*\/ x | / 0
Integral(1/(3*x - 4*sqrt(x)), (x, 0, 1))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is .
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | / ___\ | 1 2*log\-4 + 3*\/ x / | ------------- dx = C + ------------------- | ___ 3 | 3*x - 4*\/ x | /
2*log(3) 2*log(4/3) - -------- - ---------- 3 3
=
2*log(3) 2*log(4/3) - -------- - ---------- 3 3
-2*log(3)/3 - 2*log(4/3)/3
Use the examples entering the upper and lower limits of integration.