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(A) To integrate $\int \sin(mx) \, dx$,we use the method of substitution.Let $t = mx$. Then,differentiating both sides with respect to $x$,we get $dt

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$-\frac{1}{m} \cos(mx) + C$

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(A) To integrate $\int \sin(mx) \, dx$,we use the method of substitution.Let $t = mx$. Then,differentiating both sides with respect to $x$,we get $dt = m \, dx$,which implies $dx = \frac{1}{m} \, dt$.Substituting these into the integral:$\int \sin(mx) \, dx = \int \sin(t) \cdot \frac{1}{m} \, dt$$= \frac{1}{m} \int \sin(t) \, dt$$= \frac{1}{m} (-\cos(t)) + C$$= -\frac{1}{m} \cos(mx) + C$

Integrate the following function with respect to $x:$
$\sin(mx)$

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Integrate the following function with respect to $x:$$\sin(mx)$