Search for: Let I=∫exe4x+e2x+1dx,J=∫e−xe−4x+e−2x+1dx, Then, for an arbitrary constant C, the value of J-I equals Let I=∫exe4x+e2x+1dx,J=∫e−xe−4x+e−2x+1dx, Then, for an arbitrary constant C, the value of J-I equals A12loge4x−e2x+1e4x+e2x+1+CB12loge2x+ex∣+1e2x−ex+1+CC12loge2x−ex+1e2x+ex+1+CD12loge4x+e2x+1e4x−e2x+1+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:We have, J−I=∫e3xe4x2x+e2x+1−exe4x+e2x+1dx ⇒ J−I=∫e2x−1e4x+e2x+1dex⇒ J−I=∫t2−1t4+t2+1dt, where t=ex⇒ J−I=∫1t+1t2−1dt−1t⇒ J−I=12logt+1t−1t+tt+1+C⇒ J−I=12logt2−t+1t2+t+1+C=12loge2x−ex+1e2x+ex+1+C Related content Class 9 Science MCQ Chapter 12 Sound CBSE Class 12 English MCQ with Answers (Flamingo & Vistas) CBSE Class 7 Science MCQ Questions with Answers CBSE Class 12 Subject Wise MCQ 2024-25 ICSE Class 10 Toppers List 2024 Available Tenses Worksheet for Class 10 CBSE Class 7 Science Chapter 4 Heat MCQ Questions with Answers Nephron Diagram Class 10 CBSE Class 7 Science Chapter 2 Nutrition in Animals MCQ with Answers Rabindranath Tagore Jayanti 2024