Problem
5. [-/1 Points] DETAILS SCALC9 4.5.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the indefinite integral. (Use $C$ for the constant of integration.) \[ \int \cos (7+9 t) d t \] Need Help? Read It Submit Answer
Solution
Step 1 ：Set \(u = 7+9t\), then \(du = 9dt\).
Step 2 ：Adjust the integral to account for this substitution.
Step 3 ：The integral of the function \(\cos(7 + 9t)\) with respect to \(t\) is \(\frac{\sin(7 + 9t)}{9}\).
Step 4 ：Add the constant of integration \(C\) to the result.
Step 5 ：The indefinite integral of \(\cos(7 + 9t)\) with respect to \(t\) is \(\boxed{\frac{\sin(7 + 9t)}{9} + C}\).
