Question

show teh integral of sin(lnx) by parts

Answer 1

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

Answer 2

so this is wat i hav so far
u = ln x, du = dx/x...idk wat v adn dv shud be

Answer 3

I would set u = sin(ln(x)) and dv = dx

Answer 4

so wat wud du be and v equal to

Answer 5

Let me think on this for a second.

Answer 6

Okay. Let u = sin(lnx) and dv = dx. \[du = {\cos(\ln(x)) \over x} ~ and ~ v = x\]Therefore, \[\int\limits \sin(\ln x) dx = x \sin(\ln x) - \int\limits \cos(\ln x) dx\]Now we have to integrate the cos(ln x) integrate by parts. \[\int\limits \cos( \ln x) dx = x \cos(\ln x) + \int\limits \sin(\ln x) dx\]Therefore, we get \[\int\limits \sin(\ln x) dx = {x (\sin(\ln x) - \cos( \ln x)) \over 2} + C\]

Answer 7

\[\int\limits_{}^{}1 \cdot \sin(\ln(x)) dx=x \sin(\ln(x))-\int\limits_{}^{}x \cdot \frac{1}{x} \cos(\ln(x)) dx+C\]
\[=x \sin(\ln(x))-\int\limits_{}^{}\cos(\ln(x)) dx+C\]

Answer 8

beat me to it

Answer 9

are both of ur asnwers the same but written differently

Answer 10

He went further than i did
i stopped because he finished it before me

Answer 11

we started out the same way though
we recognize that the antiderivative of 1 is x

Answer 12

why is it all divided by 2 in teh final answet

Answer 13

because he had
\[2 \int\limits_{}^{}\sin(\ln(x)) dx\]

Answer 14

m confused where teh 2 comes from thou

Answer 15

Let me elaborate. After integrating the cosine term again, we get the following \[\int\limits \sin(\ln x) dx = x \sin( \ln x) - x \cos(\ln x) - \int\limits \sin (\ln x) dx\]Notice the like terms on both sides of the equal sign.

Answer 16

OH U BROUGHT IT TO TEH OTEHR SIDE

Answer 17

to get 2 integral of sen(ln x)

Answer 18

\[\int\limits\limits \sin(\ln x) dx = x \sin(\ln x) - \int\limits\limits \cos(\ln x) dx +C\]
\[= x \sin(\ln x) -[x \cos(\ln x) + \int\limits \sin(\ln x) dx] +C\]
\[= x \sin(\ln x) -x \cos(\ln x) - \int\limits \sin(\ln x) dx +C\]
so we have so far:
\[\int\limits\limits \sin(\ln x) dx = x \sin(\ln x) -x \cos(\ln x) - \int\limits \sin(\ln x) dx +C\]

Answer 19

We get \[2 \int\limits \sin (\ln x) dx = x \sin(\ln x) - x \cos(\ln x)\] Divide by 2 and whola!

Answer 20

yep yep

Answer 21

Team work baby!

Answer 22

AWESOME job u both expalin super WELL!!
Sorry im a very visual learner so wen ppl skip steps liek my teachers i get really confused

Answer 23

Glad we could be of help. The trick to trigonometric functions is to typically integrate or derive twice. That way we are able to move it to the other side of the equals sign and eliminate it. On the other hand, natural log (ln) and exponential (e^x) functions are hard to get rid of and usually stick around. Good luck!

Answer 24

THANKS for the tip.....=)