The discussion revolves around the integral ∫cos(x)^5 / sqrt(sin(x))dx, which falls under the subject area of trigonometric integrals. Participants are exploring various approaches to simplify or solve the integral without arriving at a definitive solution.
The discussion is ongoing, with participants sharing their attempts and reasoning. There is a recognition of the challenges in applying the substitution effectively, and some guidance has been offered regarding the relationship between the variables involved. However, no consensus or resolution has been reached yet.
Participants are navigating the complexities of the integral and the implications of the trigonometric identities involved. There is an acknowledgment of the need to manage the terms resulting from the substitution, which may not be fully resolved in the current discussion.
Zondrina said:Write the integral as:
##\int \frac{cos^4(x)cos(x)}{\sqrt{sin(x)}} dx##
##= \int \frac{(1-sin^2(x))^2cos(x)}{\sqrt{sin(x)}} dx##
##u = sin(x).. du = ..##
shreddinglicks said:I see, and du = cos(x)
that takes care of my cos(x) in the numerator but it doesn't take care of the identity.