Design an Advanced U substitution problem whose answer must be exactly 6 and can be solved without using calculator?

help please asap

how advanced is "advanced"? trig substitution? polynomial roots? try and meet us halfway here.

Surely your text has examples where u has been substituted for some expression. Do something similar. Then tweak some constant so the answer comes out 6.

To design an advanced u-substitution problem with an answer of 6, let's consider the integral:

∫ (x^2 + 2x + 2) / (x + 1)^2 dx

To solve this integral without using a calculator and to obtain an answer of 6, we will need to apply u-substitution. Let's go through the steps:

Step 1: Set u = x + 1
=> x = u - 1

Step 2: Find the derivative of u with respect to x
=> du/dx = 1

Step 3: Substitute x and dx in terms of u
=> x = u - 1
=> dx = du

Step 4: Rewrite the integral using the substitutions from steps 1-3
=> ∫ ((u - 1)^2 + 2(u - 1) + 2) / u^2 du

Step 5: Simplify the expression inside the integral
=> ∫ (u^2 - 2u + 1 + 2u - 2 + 2) / u^2 du
=> ∫ (u^2 + 1) / u^2 du

Step 6: Split the integrand into two separate terms
=> ∫ u^2/u^2 du + ∫ 1/u^2 du
=> ∫ 1 du + ∫ u^-2 du

Step 7: Integrate each term separately
=> u + (-u^(-1)) + C
=> u - 1/u + C

Step 8: Substitute u back in terms of x
=> x + 1 - 1/(x + 1) + C

Step 9: Simplify the expression
=> x - 1/(x + 1) + C

Now we need to find the value of the constant C. We know that the answer to this integral should be exactly 6, so we can equate the expression above to 6 and solve for C:

x - 1/(x + 1) + C = 6

To find the value of C, we would need additional information, such as the limits of integration or any other constraints. Without these specific conditions, one cannot determine the exact value of C.