Question

integral of cos(lnx)dx

Answer 1

\[\int\limits_{?}^{?}\cos(lnx)dx\]

Answer 2

so u = lnx , du= 1/x dx

Answer 3

You can put : cos(lnx) = u and x^0 = v

Answer 4

\[\int\limits x^0 \cdot \cos(\ln(x)) \cdot dx\]

Answer 5

Now you can use Integration by parts..

Answer 6

what is du of cos(lnx)?

Answer 7

Sorry, first function is : x^0

Answer 8

so u is 1?

Answer 9

yes..

Answer 10

question why some time i have to do x^0 but some time i dont

Answer 11

nvm to do integral by part i think

Answer 12

Wait, I was right earlier..

Answer 13

what is the anti derivation of cos(lnx)?

Answer 14

Here, first function is : cos(lnx)

And second function is : 1

Answer 15

Try this now..

Answer 16

so u is cos(lnx)?

Answer 17

\[\frac{d}{dx} \cos(lnx) = -\frac{1}{x}\cdot \sin(lnx)\]

Answer 18

Yes..

Answer 19

\[\int\limits 1 \cdot dx = x\]

Answer 20

ok i got it from now on thx you

Answer 21

Note, you will have to use Parts twice here..

Answer 22

k

Answer 23

First by parts will give you:

\[\int\limits \cos(lnx) \cdot dx = x \cdot \cos(lnx) + \int\limits \sin(lnx) \cdot dx\]

Answer 24

Then again integral on right side, again first function = sin(lnx) and second function = 1.

Then do the rest..

Answer 25

i got it thx you

Answer 26

You are welcome dear.. :)