Need help with this integral
$\int sin^2(lnx)dx$
#calculus
limber rune
sonic oracleBOT
roi
bitter capeBOT
Need help with this integral
$\int sin^2(lnx)dx$
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sonic snow
Need help with this integral
$\int sin^2(lnx)dx$
Set ln(x)=u and think of the identity $sin^2(x)=\frac{1-cos(2x)}{2}$
sonic oracleBOT
Rotor
limber rune
but how do i integrate the cos function after that?
open radish
The integrand is not defined everywhere. Does your integral come from an exercise and if yes are there limits of integration?
sonic snow
The integrand is not defined everywhere. Does your integral come from an exercis...
They probably just have to find the antiderivative but you are right, better be sure
sonic snow
but how do i integrate the cos function after that?
With the change of variables you get $\int sin^{2}(u)e^{u}du$
sonic oracleBOT
Rotor
limber rune
why e^u?
sonic snow
why e^u?
With the change of variables
You have $ln(x)=u$ so $x=e^{u} $ thus $dx=e^{u}du$
sonic oracleBOT
Rotor
sonic snow
**Rotor**
Now use the identity here
The biggest difficulty here is calculating $\int \frac{cos(2u)e^{u}}{2} du$
sonic oracleBOT
Rotor
sonic snow
Which you can do via double integration by parts or you can use complex analysis and the linearity of Re:z—>Re(z) by setting cos(2x)=Re(e^{2ix})
If you don’t know the latter the former is good as well
limber rune
+close