How can I evaluate this integral?

**noppawit** · August 30th 2008, 07:09 PM

How can I evaluate this integral?

Integral sin(ln(x)) dx

If possible, can anyone show me step by step?

Thank you

**ThePerfectHacker** · August 30th 2008, 07:17 PM

Originally Posted by noppawit

How can I evaluate this integral?

Integral sin(ln(x)) dx

$\int \sin (\ln x) dx = \int e^{\ln x}\sin (\ln x)(\ln x)'dx$
By substitution you need to compute,
$\int e^t \sin t dt$

**Jhevon** · August 30th 2008, 07:17 PM

Originally Posted by noppawit

How can I evaluate this integral?

Integral sin(ln(x)) dx

If possible, can anyone show me step by step?

Thank you

one way:

write as $\int \frac xx \sin ( \ln x) ~dx$

then make the substitution $t = \ln x$

you will get the integral $\int e^t \sin t~dt$ which you would then do using integration by parts, with $u = \sin t$ (the part you differentiate) and $dv = e^t~dt$ (the part you integrate)

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