SUMMARY
The integration of the function $\int x\arctan(x)dx$ can be effectively performed using integration by parts. The recommended approach involves first integrating $\arctan(x)$ by parts, selecting $u = \arctan(x)$ and $dv = dx$. Subsequently, the integral $\int x\arctan(x)dx$ can be tackled by choosing $u = x$ and $dv = \arctan(x)dx$. This method allows for a comprehensive solution without the need for integration tables.
PREREQUISITES
- Understanding of integration by parts
- Familiarity with the arctangent function
- Basic calculus concepts
- Knowledge of differential calculus
NEXT STEPS
- Study the integration by parts technique in depth
- Explore advanced integration techniques beyond basic calculus
- Learn about the properties and applications of the arctangent function
- Investigate other integration methods that do not rely on tables
USEFUL FOR
Students and educators in calculus, mathematicians seeking to deepen their understanding of integration techniques, and anyone interested in solving complex integrals without relying on tables.