Search for: ∫3sinx+2cosx3cosx+2sinxdx is equal to ∫3sinx+2cosx3cosx+2sinxdx is equal to A513x+1213ln|3cosx+2sinx|+CB−513x−1213ln|3cosx+2sinx|+CC−513x+1213ln|3cosx+2sinx|+CD−513x+1213ln|2cosx+3sinx|+C Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Let I=∫3sinx+2cosx3cosx+2sinxdx3sinx+2cosx=Addx(3cosx+2sinx)+B(3cosx+2sinx)⇒3sinx+2cosx=A(−3sinx+2cosx)+B(3cosx+2sinx)On comparing the coefficients of sin x and cos x of both sides, we get−3A+2B=3 and 2A+3B=2⇒ B=1213 and A=−513∴ I=∫B(−3sinx+2cosx)+A(3cosx+2sinx)3cosx+2sinxdx⇒ I=A∫1dx+B∫−3sinx+2cosx3cosx+2sinxdx=Ax+B∫dtt, where t=3cosx+2sinx=Ax+Bln|t|+C=−513x+1213ln|3cosx+2sinx|+C Related content Nucleus Diagram for Class 9 Neuron Diagram Class 9 Human Heart Diagram Class 10 CBSE Class 7 Science Chapter 1 Nutrition in Plants MCQ Questions with Answers CBSE Class 9 English Worksheet – The Road not Taken 50+ GK Questions and Answers for Class 8 “Kabir Ki Sakhiyan” MCQ Questions for Class 9 Hindi with Answers Kshitij, Kritika, Sparsh, Sanchayan Bhag 1 CBSE Class 7 English Honeycomb Chapter 1 Three Questions MCQ Questions with Answers CBSE Class 9 English Beehive Book Poem 1 The Road Not Taken MCQ Questions with Answers MCQs Questions with Answers for Class 9 English Chapter 1 The Fun They Had