Final answer:
To find the integral of (x+1) root ax+b dx, use the power rule for integration and handle the root correctly.
Step-by-step explanation:
To find the integral of (x+1) root ax+b dx, we need to determine the limits of integration a and b.
Once we have the limits, we can use the power rule for integration.
The power rule states that the integral of x^n dx, where n is any real number except -1, is (1/(n+1))x^(n+1) + C, where C is the constant of integration.
In this case, the power is 1/2 since the root is square root.
So, the integral becomes (2/(1/2+1))(x+1)^(1/2+1) + C.
Simplifying the expression, we get 4(x+1)^(3/2)/3 + C.
Therefore, the integral of (x+1) root ax+b dx is 4(x+1)^(3/2)/3 + C, where C is the constant of integration.