Final answer:
To evaluate the integration ∫(1³)(9+x)² dx, we can use the substitution method. Substitute (9+x) as z and solve for the integral using the substituted variable. The final answer is (1/3)(9+x)³ + C.
Step-by-step explanation:
In this problem, you have given an integration by substitution problem. The integral to evaluate is ∫(1³)(9+x)² dx. To solve this, we can use the substitution method. Let's substitute (9+x) as z. Therefore, z = 9 + x. Taking the derivative of both sides, dz/dx = 1, which implies dx = dz. Now the integral becomes ∫z² dz. Integrating z² with respect to z, we get (1/3)z³ + C, where C is the constant of integration. Substituting z back with (9+x), the final answer is (1/3)(9+x)³ + C.