Painguy said:Homework Statement
∫cot^2(x)csc^4(x)dx
Homework Equations
The Attempt at a Solution
∫cot^2(x)(cot^2(x)+1)csc^2(x)dx
u=cot(x)
du=-csc^2(x)dx
-∫u^2 (u^2 +1)du
-∫u^4 + 2u^3 + u^2 du
-(u^5)/5 - (u^4)/2 - (u^3)/3
-cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C
Wolfram alpha shows the solution as -cot^5(x)/5 - cot^3(x)/3 + C
So I'm unsure as to how I got the cot^4(x)/2
What exactly did I do wrong or is wolfram wrong?
Thanks in advance
Trigonometric substitution is a technique used in calculus to simplify integrals involving radical expressions. It involves substituting a trigonometric function for a variable in the integral in order to transform it into a simpler form.
Trigonometric substitution should be used when the integral involves a radical expression that can be rewritten in terms of a trigonometric function. This technique is especially useful when dealing with integrals containing square roots or the quadratic formula.
The trigonometric function to substitute is chosen based on the form of the radical expression in the integral. For example, if the integral contains a term of the form sqrt(a^2 - x^2), then the substitution x = a*sin(theta) would be appropriate.
Some common mistakes when using Trigonometric Substitution include forgetting to change the limits of integration, using the wrong trigonometric function to substitute, and not simplifying the integral after substitution. It is important to carefully check each step and make sure the final answer is in its simplest form.
Yes, there are other methods for solving integrals involving trigonometric functions, such as integration by parts and u-substitution. However, Trigonometric Substitution is particularly useful for integrals with radical expressions and can often lead to simpler solutions.