Problem
10. $[-/ 1$ Points] DETAILS SCALC9 4.4.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the general indefinite integral. (Use $C$ for the constant of integration.) \[ \int(5 x+\cos (x)) d x \] Need Help? Read It Submit Answer
Solution
Step 1 ：Split the integral into two parts: the integral of 5x and the integral of cos(x).
Step 2 ：The integral of 5x is \(\frac{5}{2}x^2\).
Step 3 ：The integral of cos(x) is sin(x).
Step 4 ：Add a constant of integration, C, to the result.
Step 5 ：So, the general indefinite integral of the function \(5x + \cos(x)\) is \(\frac{5}{2}x^2 + \sin(x) + C\).
Step 6 ：\(\boxed{\frac{5}{2}x^2 + \sin(x) + C}\) is the final answer.
