Answer:
Scroll Down Below...
Explanation:
To judge the necessary ∫(cos^5x / bunk^5x) dx, we can facilitate the integrand utilizing concerning manipulation of numbers identities.First, we revise bunk^5x as (cosx / sinx)^5 and streamline:∫(cos^5x / bunk^5x) dx = ∫(cos^5x / (cosx / sinx)^5) dx = ∫(cos^5x * sin^5x / cos^5x) dx = ∫sin^5x dxNow we can use a concerning manipulation of numbers correspondence to further reduce sin^5x. We have:sin^5x = (1 - cos^2x)^2 * sinx = (1 - cos^2x)(1 - cos^2x) * sinx = (1 - cos^2x)(sin^2x) * sinx = sin^3x - sinx * cos^2xNow we can revise the complete as:∫sin^5x dx = ∫(sin^3x - sinx * cos^2x) dxWe can mix each term alone:∫sin^3x dx = (-1/3) * cos^3x + C1∫(sinx * cos^2x) dx = (1/3) * cos^3x + C2Where C1 and C2 are unification continuous.Therefore, the resolution to the elemental is:∫(cos^5x / bunk^5x) dx = ∫sin^5x dx = (-1/3) * cos^3x + C1 - (1/3) * cos^3x + C2 = -(2/3) * cos^3x + CWhere C = C1 + C2 is the ending unification loyal.