Question

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

Answer 1

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

Answer 2

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

Answer 3

yes it is.

Answer 4

@zepdrix

Answer 5

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,\[\large\rm e^{\ln x}=x\]

Answer 6

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

Answer 7

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

Answer 8

ahh! got it!! thank you @zepdrix

Answer 9

Got it? :) Cool

Answer 10

thanks!

Answer 11

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