- #1
juantheron
- 243
- 1
$\displaystyle \int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$
Inverse Integral: $\int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$
Click For Summary
SUMMARY
The integral $\int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$ is evaluated using integration by parts. The choice of $dv = \frac{x^2}{(1-x^3)^2}dx$ and $u = \cos^{-1}(x\sqrt{x})$ is critical for simplifying the expression. This method effectively reduces the complexity of the integral, allowing for further analysis and computation. The discussion emphasizes the importance of strategic variable selection in integration techniques.
PREREQUISITES- Integration by parts
- Understanding of inverse trigonometric functions
- Knowledge of polynomial functions and their derivatives
- Familiarity with limits and continuity in calculus
- Study advanced integration techniques, focusing on integration by parts
- Explore the properties and applications of inverse trigonometric functions
- Learn about the behavior of rational functions and their integrals
- Investigate the use of substitution methods in complex integrals
Students and professionals in mathematics, particularly those focusing on calculus and integral evaluation techniques. This discussion is beneficial for anyone looking to deepen their understanding of integration methods and their applications.
Similar threads
- · Replies 12 ·
- · Replies 4 ·
- · Replies 2 ·
- · Replies 6 ·
- · Replies 8 ·
Undergrad
Another Integration Formula
- · Replies 6 ·
Undergrad
Substitution in a definite integral
- · Replies 6 ·
- · Replies 4 ·
- · Replies 3 ·
Undergrad
Find ##\int_0^π \sin^ n x dx ##
- · Replies 5 ·