Use the table of antiderivatives to determine if the following statement is true. $\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C$

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The given integral can be solved using the method of integration by parts or looking it up in a table of antiderivatives for functions of the form $e^{ax}\cos(bx)$ or $e^{ax}\sin(bx)$, where the result involves a linear combination of $e^{ax}\cos(bx)$ and $e^{ax}\sin(bx)$ multiplied by a constant. The constant $\frac{1}{113}$ correctly normalizes the coefficients to account for the derivatives of the cosine and sine functions multiplied by $e^{7x}$, making the statement true.

Use the Table of Antiderivatives to Determine If the Following ∫e7xcos⁡8xdx=1113e7x(7cos⁡8x+8sin⁡8x)+C\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C∫e7xcos8xdx=1131​e7x(7cos8x+8sin8x)+C

Use the Table of Antiderivatives to Determine If the Following $\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C$