Q. The value of $\int_{}^{}{e^{2x}(2\sin{3x + 3\cos{3x)dx}}}$ is
A) $e^{2x}\sin{3x + c}$
B) $e^{2x}\cos{3x + c}$
C) $e^{2x} + c$
D) $e^{2x}\ (2\sin{3x) + c}$
Explanation
(a)
$\int_{}^{}{e^{2x}(2\sin{3x + 3\cos{3x)dx}}}$
$= 2\int_{}^{}{e^{2x}\sin{3x + dx + 3\int_{}^{}{e^{2x}\cos{3x\ dx}}}}$
$= e^{2x}\sin{3x - 3\int_{}^{}{e^{2x}\cos{3x\ dx + 3\int_{}^{}{e^{2x}\cos{3x\ dx}}}}}$
$= e^{2x}\sin{3x + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.