SolutionWe know the integral of sinx and lnx but not of sin(lnx). Also we can see the derivative of lnx in the integrand.
So we assume t=lnx
Thus, our integral becomes
∫sin t dt=−cos(t)+C
Also we know that the constant of integration is taken as 0
Thus substituting back t and taking C as 0.
We get f(x)=−cos(lnx)