SUMMARY
The integral ∫arctan(√x)dx can be solved using the substitution √x=t, leading to the transformation ∫arctan(t)dt2. The confusion regarding the squared dt arises from the differentiation of t², where dx=d(t²)=2tdt. This method employs "integration by substitution" followed by "integration by parts," resulting in the expression 2∫arctan(t)tdt, which is the correct approach for solving the integral.
PREREQUISITES
- Understanding of integral calculus
- Familiarity with integration by substitution
- Knowledge of integration by parts
- Basic algebraic manipulation skills
NEXT STEPS
- Study the method of integration by substitution in detail
- Learn the technique of integration by parts
- Practice solving integrals involving arctangent functions
- Explore advanced integration techniques for complex functions
USEFUL FOR
Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of integration techniques.