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Question

# Find each integral. $\int(3 \cos x-4 \sin x) d x$

Solution

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$\begin{gathered} \int {\left( {3\cos x - 4\sin x} \right)} dx \\ \textcolor{#4257b2}{{\text{Rewrite as two integrals}}} \\ = \int {3\cos x} dx - \int {4\sin x} dx \\ \textcolor{#4257b2}{ {\text{Pull out the constants}}} \\ = 3\int {\cos x} dx - 4\int {\sin x} dx \\ \textcolor{#4257b2}{{\text{Integrate}}} \\ = 3\left( {\sin x} \right) - 4\left( { - \cos x} \right) + C \\ \textcolor{#4257b2}{{\text{Simplify}}} \\ = 3\sin x + 4\cos x + C \\ \end{gathered}$

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