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anonymous
 5 years ago
solve this integration in details using integration by parts:(−e−x)cosxdx
anonymous
 5 years ago
solve this integration in details using integration by parts:(−e−x)cosxdx

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits (e ^{x})cosx dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits (e ^{x})cosx dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}udv=uv\int\limits_{}^{}vdu\] u=cos(x) \[dv=e^{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so: \[\int\limits_{}^{}e ^{x}\cos(x)dx=e ^{x} \cos(x)\int\limits_{}^{}e^{x}\sin(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and u=sin(x) dv=e^(x) so: \[\int\limits_{}^{}e^{x}\cos(x)dx=e^{x}\cos(x)e^{x}\sin(x)+\int\limits_{}^{}e^{x}\cos(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0subtract \[\int\limits_{}^{} e^{x}\cos(x) \] from both sides: \[2\int\limits_{}^{}e^{x}\cos(x)=e^{x}\cos(x)e^{x}\sin(x)\] divide each side by 2: \[\int\limits\limits_{}^{}e^{x}\cos(x)=(1/2)(e^{x}\cos(x)e^{x}\sin(x))+C\]
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