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Integration by substitution , Exams of Mathematics

Al-Aqsa UniversityMathematics

Integration by substitution using trigonometric functions

Typology: Exams

2016/2017

Uploaded on 10/18/2017

OSAMA-ALSATTARI
OSAMA-ALSATTARI 🇵🇸

4.6

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5 sin2x — sin*xtanx Evaluate: [ Se cos?x — 3sin?x Solution: [ 3sinxcos x cosx(cos*x ees el cos*x)) Thus, | Z 3 x— six sinx(3cos?x —-1i+ cos*x) cosx(cos*x — 3 4+ 3cos*x) 4y? -1 OSES, as { yy? —3 + 3y*) Se : 3 sin2x — sin? xtanx 4y3 As aresult, MR. OSAMA A.A. ALSATTARI cos*x — 3sin*x dx Let y = cosx => dx = — Ay" dx dy SINX -—1 dy 1 Ce — 3 in(4cos*x — 3cosx) +c