Search for: The integral ∫2x−3×2+x+12 dx is equal to The integral ∫2x−3x2+x+12 dx is equal to A−1x2+x+1−1633tan−12x+13−432x+1x2+x+1+CB−1x2+x+1−1633tan−12x-13+432x-1x2+x+1+CC12x2+x+1−(2x+1)2x2+x+12+CD14x2+x+1+23tan−1(2x+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, I=∫2x−3x2+x+12dx=∫(2x+1)−4x2+x+12dx⇒I=∫2x+1x2+x+12dx−4∫1(x+1/2)2+(3/2)22dx I=−1x2+x+1−4I1 where I1=∫1[(x+1/2)2+(3/2)2]2dx Putting x+1/2=(3/2) tanθ in I1, We get I1=∫3/2sec2θdθ[(3/2)tanθ)]2+(3/2)22⇒ I1=833∫cos2θdθ=833∫1+cos2θ2dθ⇒ I1=433{θ+12sin2θ}+C⇒ I1=433tan−12x+13+122tanθ1+tan2θ+C⇒ I1=433tan−12x+13+342x+1x2+x+1+C∴ I=−1x2+x+1−1633tan−12x+13−432x+1x2+x+1+C Related content VITEEE Result 2024 Announce on the official website – viteee.vit.ac.in NEET Marks vs Rank 2024 – Check NEET Rank vs Marks vs Percentile Analysis Complex Numbers Class 11 Worksheet with Answers CBSE 12th Result 2024 (Out) Today, How to check CBSE Class 12 Marks @cbseresults.nic.in How to use NEET UG College Predictor 2024 to find your dream Medical College Is a Gap Certificate for NEET Repeaters Necessary? General Knowledge Questions With Answers on Islamic CBSE Class 10 Worksheets NEET Rank Predictor 2024: Calculate Your Rank by Marks Why to Choose Infinity Learn NEET Rank Predictor 2024 – The Most Accurate NEET Rank Predictor