The discussion focuses on finding the antiderivative of the expression x^5 + tan(2x)sec(2x)dx. Participants emphasize the necessity of using u-substitution twice to simplify the integration process. One user suggests changing the trigonometric functions to sine and cosine before applying substitutions, specifically letting u = cos(x) and du = -sin(x). The conversation highlights the importance of analyzing the equation thoroughly before attempting manipulation to avoid unnecessary complexity.
PREREQUISITESStudents and educators in calculus, particularly those focusing on integration techniques and antiderivatives. This discussion is beneficial for anyone looking to enhance their understanding of trigonometric integration methods.
donjt81 said:problem: find the anti derivative of x^5 + tan(2x)sec(2x)dx
how do you find the anti derivative of the second half of that problem tan(2x)sec(2x)
prace said:yeah, you are going to have to use u-substitution twice. I don't know if I am correct or not, but I changed everything to sin and cos before anything and manipulated it that way. I then let u = cosx and du = -sinx. For the second u-substitution, I let v=u²-1 and (1/2)dv = udu. I hope that helps and does not confuse you and more.