Final answer:
To evaluate the indefinite integral using the substitution u = 11 - 5x, differentiate the substitution to find du, replace x and dx in the integral with u and du, and integrate with respect to u before substituting back.
Step-by-step explanation:
To evaluate the indefinite integral with the substitution u = 11 - 5x, follow these steps:
- Start with the given substitution u = 11 - 5x and differentiate to find du, leading to du/dx = -5 or du = -5dx.
- Rearrange du = -5dx to solve for dx: dx = du/(-5).
- Replace all instances of x and dx in the integral with u and du/(-5), respectively.
- Integrate the function with respect to u, considering the antiderivative of the new terms formed after substitution.
- Finally, substitute u back for 11 - 5x in the antiderivative to get the result in terms of x.
This process will provide the solution to the integral using the substitution method.