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Question

Question: \(\int_{}^{}e^{–2x}\) sin 3x dx =...

e2x\int_{}^{}e^{–2x} sin 3x dx =

A

113\frac{1}{13} e–2x [sin 3x + cos 3x ] + c

B

113\frac{1}{13}e–2x [sin3x + cos 3x] + c

C

113\frac{1}{13}e–2x [2sin 3x + 3 cos 3x] + c

D

113\frac{1}{13}e–2x [2sin 3x + 3 cos 3x] + c

Answer

113\frac{1}{13}e–2x 2sin3x+3cos3x2sin 3x + 3 cos 3x + c

Explanation

Solution

Use formula eax.sin(bx+c)\int_{}^{}{e^{ax}.\sin(bx + c)}dx

= [a sin(bx + c) – b cos(bx + c)] + c