If you have written the integrals exactly as they were given, they should all be very easy. The variable of integration in all three is t (based on the dt part).nysnacc said:
Integration by parts is a technique used in calculus to evaluate integrals of products of functions. It involves choosing one function as the "u" function and another as the "dv" function, and then using the formula ∫udv = uv - ∫vdu to find the integral.
Integration by parts may not work for certain integrals because it relies on finding a "u" and "dv" function that can be easily integrated. If these functions cannot be easily integrated, the method will not be effective.
There are a few signs that integration by parts may be successful on a given integral. These include the presence of a product of functions, the presence of an inverse trigonometric function, or the presence of a logarithmic function.
If integration by parts is not working on a given integral, there are other techniques that can be used, such as u-substitution or partial fraction decomposition. It may also be helpful to try a different choice for the "u" and "dv" functions.
Yes, there are a few common mistakes that can be made when using integration by parts. These include incorrect integration of the "u" and "dv" functions, forgetting to include the negative sign in the formula, and not simplifying the resulting integral properly.