Q13. Evaluate the Integral $\int e^{-3x} \cos(2x)dx$ using Integration by Parts. [5]
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Let u = e^-x and dv = cos(2kx) dx. Then, we have du/dx = -e^-x and v = (1/2k) sin(2kx). Using the integration by parts formula, we have: ∫ e^-x cos(2kx) dx = u*v - ∫ v*du/dx dx = e^-x (1/2k) sin(2kx) - ∫ (1/2k) sin(2kx) (-e^-x) dx = e^-x (1/2k) sin(2kx) + (1/2k) Show more…
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