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

question 124

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

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