Mathematics

Mathematics

Problem

The answers are in Chapter 24. 5. Evaluate ∫ex2cos⁡(2x)dx\int e^{\frac{x}{2}} \cos (2 x) d x. (A) 1716[ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\frac{17}{16}\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (B) [ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (C) [ex2sin⁡(2x)2−ex2cos⁡(2x)8]+C\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}-\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (D) 1617[ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\frac{16}{17}\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (A) 1716[ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\frac{17}{16}\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (B) [ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (C) [ex2sin⁡(2x)2−ex2cos⁡(2x)8]+C\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}-\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C (D) 1617[ex2sin⁡(2x)2+ex2cos⁡(2x)8]+C\frac{16}{17}\left[\frac{e^{\frac{x}{2}} \sin (2 x)}{2}+\frac{e^{\frac{x}{2}} \cos (2 x)}{8}\right]+C

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