Question

$\int e^{3x}\cos 4xdx$ is equal to
( where $C$ is the constant of integration)

• A. $\frac{e^{3x}}{25}(3\cos 4x+4\sin 4x)+C$
• B. $\frac{e^{2x}}{25}(3\cos 4x-4\sin 4x)+C$
• C. $\frac{e^{3x}}{16}(3\cos 4x+4\sin 4x)+C$
• D. $\frac{e^{3x}}{25}(4\cos 4x+3\sin 4x)+C$

Answer 1

The correct option is A $\frac{e^{3x}}{25}(3\cos 4x+4\sin 4x)+C$

$I=\int e^{3x}\cos 4xdx\Rightarrow I=\frac{e^{3x}}{3^2+4^2}(3\cos 4x+4\sin 4x)+C(\because \int e^{ax}\cos bx=\frac{e^{ax}}{a^2+b^2}(a\cos bx+b\sin bx))\therefore I=\frac{e^{3x}}{25}(3\cos 4x+4\sin 4x)+C$