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