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DETAILS SCALC9 4.5.017.
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Evaluate the indefinite integral. (Use $C$ for the constant of integration.)
\[
\int \cos (7+9 t) d t
\]
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Answer

The indefinite integral of $\cos(7 + 9t)$ with respect to $t$ is $\boxed{\frac{\sin(7 + 9t)}{9} + C}$.

Steps

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 $\boxed{\frac{\sin(7 + 9t)}{9} + C}$.