The value of

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of ∫e(xsin⁡x+cos⁡x)⋅(x4cos⁡3x−xsin⁡x+cos⁡xx2cos⁡2x)dx\int e^{(x \sin x + \cos x)} \cdot \left( \frac{x^4 \cos^3 x - x \sin x + \cos x}{x^2 \cos^2 x} \right) dx , is equal to (1) e(xsin⁡x+cos⁡x)⋅(x+1xcos⁡x)+Ce^{(x \sin x + \cos x)} \cdot \left( x + \frac{1}{x \cos x} \right) + C (2) e(xsin⁡x+cos⁡x)⋅(xcos⁡x+1x)+Ce^{(x \sin x + \cos x)} \cdot \left( x \cos x + \frac{1}{x} \right) + C (3) e(xsin⁡x+cos⁡x)⋅(x−1xcos⁡x)+Ce^{(x \sin x + \cos x)} \cdot \left( x - \frac{1}{x \cos x} \right) + C (4) None of the above

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