Ask your own question, for FREE!
Mathematics 24 Online
OpenStudy (kunalgohrani):

integation {e^(log x)+sin x}cos x dx

OpenStudy (luffingsails):

try multiplying through by cos(x) and then integrating each of the components separately.

zepdrix (zepdrix):

This is your integral?\[\large\rm \int\limits (e^{\ln x}+\sin x)\cos x~dx\]

OpenStudy (kunalgohrani):

yes it is.

OpenStudy (kunalgohrani):

@zepdrix

zepdrix (zepdrix):

Recall that the exponential and log are inverse operations of one another, so taking their composition will give us the argument back as a result,\[\large\rm e^{\ln x}=x\]

zepdrix (zepdrix):

\[\large\rm \int\limits\limits (x+\sin x)\cos x~dx\]

zepdrix (zepdrix):

Distribute the cosx as Luff indicated,\[\large\rm \int\limits x \cos x~dx+\int\limits \sin x \cos x~dx\]

OpenStudy (kunalgohrani):

ahh! got it!! thank you @zepdrix

zepdrix (zepdrix):

Got it? :) Cool

OpenStudy (kunalgohrani):

thanks!

zepdrix (zepdrix):

\(\Large\rm \color{royalblue}{\text{Welcome to OpenStudy! :)}}\)

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!