integrate by parts:
ʃ sinx lnx

Question

integrate by parts:
ʃ sinx lnx

turingtest · Answer

I don't think this is expressible in terms of elementary functions

amistre64 · Answer

can you cycle it back around?

amistre64 · Answer

sin(x)
+ ln(x)     cos(x)
- 1/x      -sin(x)

hmmm

turingtest · Answer

the way I see it:
dv=sin x
u=lnx

u never goes away

the other way, u=lnx, does not seem promising, but give it a try :D

turingtest · Answer

the other way dv=lnx I mean...

amistre64 · Answer

ln(x) ups to what:  xln(x) - x i think

anonymous · Answer

lnx cant be integrated right?

amistre64 · Answer

amistre64 · Answer

yes, lnx can be integrated

amistre64 · Answer

xlnx - x derives to

ln(x) + x/x - 1 = ln(x)

amistre64 · Answer

$$\int sin(x)ln(x)dx= sin(x)(xln(x)-x) - \int cos(x)(xlnx-x) dx$$ 
$$\int cos(x)(xlnx-x) dx=\int xcos(x)ln(x)-xcos(x)\ dx$$

amistre64 · Answer

its ugly, but might be doable overall

anonymous · Answer

lnx cant be differentiated?

amistre64 · Answer

otherwise:
$$\int sin(x)ln(x)dx=cos(x)ln(x)-\int \frac{cos(x)}{x}dx$$

amistre64 · Answer

really?  ln(x)' = 1/x

amistre64 · Answer

you need to brush up on this stuff i assume lol

anonymous · Answer

lnx cant be integrated im sure. it is non-integrable

turingtest · Answer

lnx is totally integrable by parts, as amistre did above

turingtest · Answer

$$\int \ln xdx$$$$u=\ln x$$$$dv=1$$try it!

anonymous · Answer

differntial of lnx=1/x.... but what is the answer of integral of lnx? just the final answer?

turingtest · Answer

um... the final answer is the final answer, not sure what you mean