Integral (6x+5) root of (6-2x+x²) dx

This is a complex integral problem that requires knowledge of calculus. Here's a step-by-step solution:

Step 1: Recognize the integral as a standard form The integral is in the form ∫f'(x)√(f(x)) dx, where f(x) = 6 - 2x + x² and f'(x) = 6x + 5.

Step 2: Use the formula The integral of this form can be solved using the formula ∫f'(x)√(f(x)) dx = 2/3 * (f(x))^(3/2) + C, where C is the constant of integration.

Step 3: Substitute f(x) into the formula Substitute f(x) = 6 - 2x + x² into the formula to get the solution: 2/3 * (6 - 2x + x²)^(3/2) + C.

So, the integral ∫(6x+5)√(6-2x+x²) dx = 2/3 * (6 - 2x + x²)^(3/2) + C.