find the most general antiderivative or indefinite integral. ∫(6 cos 6w - 5 sin 5w) dw ∫(6 cos 6w - 5 sin…

Explanation:

Step1: Split the integral

By the property $\int(f(x)\pm g(x))dx=\int f(x)dx\pm\int g(x)dx$, we have $\int(6\cos6w - 5\sin5w)dw=\int6\cos6w dw-\int5\sin5w dw$.

Step2: Integrate $\int6\cos6w dw$

Let $u = 6w$, then $du=6dw$. So $\int6\cos6w dw=\int\cos u du=\sin u + C_1=\sin6w + C_1$.

Step3: Integrate $\int5\sin5w dw$

Let $v = 5w$, then $dv = 5dw$. So $\int5\sin5w dw=-\int(- 5\sin5w)dw=-\cos v + C_2=-\cos5w + C_2$.

Step4: Combine the results

$\int(6\cos6w - 5\sin5w)dw=\sin6w+\cos5w + C$, where $C = C_1 + C_2$.

Answer:

$\sin6w+\cos5w + C$