COMEDK · Maths · 28. Indefinite Integration
\(\int e^{2x}\cos(5x + 3)dx =\)
- A \(\dfrac{e^{2x}}{29}[5\cos(5x+3) - 2\sin(5x+3)] + C\)
- B \(\dfrac{e^{2x}}{29}[2\cos(5x+3) - 5\sin(5x+3)] + C\)
- C \(\dfrac{e^{2x}}{29}[2\cos(5x+3) + 5\sin(5x+3)] + C\)
- D \(\dfrac{e^{2x}}{29}[2\sin(5x+3) + 5\cos(5x+3)] + C\)
Answer & Solution
Correct Answer
(C) \(\dfrac{e^{2x}}{29}[2\cos(5x+3) + 5\sin(5x+3)] + C\)
Step-by-step Solution
Detailed explanation
Using the standard integral formula: \(\int e^{ax}\cos(bx + c)dx = \dfrac{e^{ax}}{a^2 + b^2}[a\cos(bx + c) + b\sin(bx + c)] + C\) Comparing the given integral \(\int e^{2x}\cos(5x + 3)dx\) with the standard form, we get \(a = 2\), \(b = 5\), and \(c = 3\). Substituting these…
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