2 x / | | (x - 3*y) dy | / ___ -\/ x ------- 1 + x
Integral(x - 3*y, (y, -sqrt(x)/(1 + x), x^2))
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
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:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 2 | 3*y | (x - 3*y) dy = C - ---- + x*y | 2 /
4 3/2 3 3*x x 3*x x - ---- + ----- + ---------- 2 1 + x 2 2*(1 + x)
=
4 3/2 3 3*x x 3*x x - ---- + ----- + ---------- 2 1 + x 2 2*(1 + x)
x^3 - 3*x^4/2 + x^(3/2)/(1 + x) + 3*x/(2*(1 + x)^2)
Use the examples entering the upper and lower limits of integration.