COMEDK · Maths · 28. Indefinite Integration
\(\int e^{x}(\cos x-\sin x) d x\) is equal to
- A \(e^{x} \cos x+C\)
- B \(e^{x} \sin x+C\)
- C \(-e^{x} \cos x+C\)
- D \(-e^{x} \sin x+C\)
Answer & Solution
Correct Answer
(A) \(e^{x} \cos x+C\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \text{Let} \quad I &=\int e^{x}(\cos x-\sin x) d x \\ &=\int e^{x} \cos x d x-\int e^{x} \sin x d x \\ &=\int e^{x} \cos x d x-\left[e^{x}(-\cos x)-\int e^{x}(-\cos x) d x\right] \\ &=\int e^{x} \cos x d x+e^{x} \cos x-\int e^{x} \cos x d x \\ &=e^{x} \cos x+C…
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