Integration by parts is a mathematical method used to solve integrals that involve a product of two functions. It is based on the product rule of differentiation and involves breaking down the integral into simpler parts that can be easily solved.
You should use integration by parts when the integral involves a product of two functions, and you are unable to solve it using other methods such as substitution or partial fraction decomposition.
The formula for integration by parts is ∫u*dv = uv - ∫v*du, where u and v are the two functions in the integral and du and dv are their respective differentials.
To solve this integral, you can follow these steps:
1. Identify u and dv by rewriting the integrand as u*dv.
2. Calculate du and v by taking the derivatives and antiderivatives of u and dv, respectively.
3. Substitute the values of u, du, dv, and v into the integration by parts formula.
4. Simplify the resulting integral and solve for the final answer.
Practice is key when it comes to mastering integration by parts. It is also helpful to have a good understanding of the product rule of differentiation and to carefully choose which function to assign as u and which as dv. Additionally, breaking down the integral into smaller parts and using substitution or other methods when possible can make the process easier.