1. $[-13$ Points $]$ DETAILS SCALC9 4.5.001.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following integral. \[ \int \cos (4 x) d x \] Given the substitution $u=4 x$, find $d u$. \[ d u=(\square) d x \] Rewrite the given integral in terms of $u$. Evaluate the integral by making the given substitution. (Use $C$ for the constant of integration.) Need Help? Read It Submit Answer

Step 1 ：Given the substitution $u=4x$, we find $du$ by taking the derivative of $u$ with respect to $x$, multiplied by $dx$. Therefore, $du = 4dx$.

Step 2 ：We rewrite the given integral in terms of $u$. The integral is currently $\int \cos(4x) dx$. We substitute $u$ for $4x$, and $\frac{du}{4}$ for $dx$, to get $\int \cos(u) \frac{du}{4}$.

Step 3 ：We evaluate the integral. The integral of $\cos(u)$ is $\sin(u)$, so the integral of $\cos(u) \frac{du}{4}$ is $\frac{\sin(u)}{4} + C$, where $C$ is the constant of integration. After substituting $u$ back in terms of $x$, the final answer is $\boxed{\frac{\sin(4x)}{4} + C}$.