Question

use integration by parts to compute the following integral, please show steps!!!
integrate: sin(3lnx)dx

Answer 1

\[t=\ln x\]
\[x=e^{t}\]
\[result=\int\limits_{}^{}\sin t e^{t}dt =\int\limits_{}^{}0.5(\sin t +\cos t+\sin t -\cos t )e^{t}dt\]
\[ =0.5 \int \limits_{}^{}\sin t e^{t} + \cos t e^{t}dt+0.5 \int \limits_{}^{}\sin t e^{t} - \cos t e^{t}dt\]
\[=0.5 (\sin t e^{t} - \cos t e^{t}) \]
\[=0.5 x(\sin \ln x - \cos \ln x) \]

Answer 2

what happened to the 3?