Search for: If ∫sec4/3xcosec8/3xdx=a(tanx)−5/3+b(tanx)1/3+C, then 5a+b=If ∫sec4/3xcosec8/3xdx=a(tanx)−5/3+b(tanx)1/3+C, then 5a+b=A3B-3C0D-1 Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:We have, I∫sec4/3xcosec8/3xdx⇒ I=∫cos−4/3xsin−8/3xdx=∫1cos4/3xsin8/3xdxThe sum of the exponents of sin x and cos x is - 4, an even integer. So, we divide both numerator and denominator by cos4x.∴ I =∫sec4xtan8/3xdx=∫1+tan2x(tanx)−8/3d(tanx)⇒ I =∫(tanx)−8/3+(tanx)−2/3d(tanx)⇒ I =−35(tanx)−5/3+3(tanx)1/3+C∴ a=−35 and b=3⇒5a+b=0Post navigationPrevious: The value of ∫0π |cosx|dx is Next: ∫exloga⋅exdx is equal toRelated content JEE Main 2023 Session 2 Registration to begin today JEE Main 2023 Result: Session 1 NEET 2024 JEE Advanced 2023 NEET Rank Assurance Program | NEET Crash Course 2023 JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria