# Thread: How can I evaluate this integral?

1. ## How can I evaluate this integral?

How can I evaluate this integral?

Integral sin(ln(x)) dx

If possible, can anyone show me step by step?

Thank you

2. Originally Posted by noppawit
How can I evaluate this integral?

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

3. 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 $\displaystyle \int \frac xx \sin ( \ln x) ~dx$

then make the substitution $\displaystyle t = \ln x$

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