Integrating int sin(ln(x)) involves using the substitution method, where you substitute u=ln(x) and du=dx/x to turn the integral into int sin(u)du. From there, you can use the integration by parts method to solve the integral.
No, there is no specific formula for integrating int sin(ln(x)). It requires using the substitution and integration by parts methods to solve the integral.
Sure, let's say we have the integral int sin(ln(x))dx. We can substitute u=ln(x) to get int sin(u)du. Then, using integration by parts with u=sin(u) and dv=du, we get the final result of -cos(ln(x))+C.
Yes, the substitution and integration by parts methods are commonly used to solve integrals involving trigonometric and logarithmic functions. Additionally, using trigonometric identities or rewriting the integral in a different form may also be helpful.
One common mistake is forgetting to substitute for u=ln(x) and attempting to integrate the original integral. It is also important to pay attention to the limits of integration and make sure they are adjusted accordingly after the substitution. Additionally, care must be taken when using integration by parts to avoid errors in the calculation.