Evaluate the Integral Using Integration by Parts $\int e ^ { a x } \cos b x d x$

Multiple Choice

Evaluate the integral using integration by parts.
- $\int e ^ { a x } \cos b x d x$

A) $\frac { 1 } { 2 b }$ $\mathrm { e } ^ { \mathrm { ax } }$ $\cos ^ { 2 }$ bx + C
B) $\mathrm { e } ^ { \mathrm { ax } }$ (sin bx - cos bx) + C
C) $\mathrm { e } ^ { \mathrm { ax } }$ $\left( \frac { b \sin b x + a \cos b x } { a ^ { 2 } + b ^ { 2 } } \right)$ + C
D) $\mathrm { e } ^ { \mathrm { ax } }$ (sin bx + cos bx) + C