#14. ### Integration by Parts: Practice ProblemsIn calculus, integration by parts is a technique used to evaluate integrals involving the product of functions. Below are two problems that can be solved using this method.#### Problem 13**Use integration by parts to evaluate the integral:**\[ \int (3x + 2) \cos (2x) \, dx \]*Hint*: Let \(u = 3x + 2\) and \(dv = \cos (2x) \, dx\).#### Problem 14**Use integration by parts to evaluate the integral:**\[ \int_{0}^{\ln{2}} x e^x \, dx \]*Hint*: Let \(u = x\) and \(dv = e^x \, dx\).Follow the process of integration by parts:\[ \int u \, dv = uv - \int v \, du \]**Explanation:** Break down the integrals by identifying parts matched to \( u \) and \( dv \), differentiate and integrate to find corresponding \( du \) and \( v \), then apply the integration by parts formula to solve.

Name: #14. ### Integration by Parts: Practice ProblemsIn calculus, integrati
Uploaded: 2024-03-20T06:46:55.000Z
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Description: #14. ### Integration by Parts: Practice ProblemsIn calculus, integration by parts is a technique used to evaluate integrals involving the product of functions. Below are two problems that can be solved using this method.#### Problem 13**Use integrati