CBSE Class 12-science Answered
integrate dx/x(6(logx) ^2 +7logx +2)
Asked by sidhusoni115 | 03 Oct, 2020, 08:08: AM
TO integrate dx/x(6(log x)2 + 7 logx + 2)
![straight I equals integral fraction numerator dx over denominator straight x open square brackets 6 open parentheses logx close parentheses squared plus 7 logx plus 2 close square brackets end fraction
Take space logx equals straight y rightwards double arrow straight x equals straight e to the power of straight y rightwards double arrow dx equals straight e to the power of straight y dy
rightwards double arrow straight I equals integral fraction numerator straight e to the power of straight y dy over denominator straight e to the power of straight y open square brackets 6 straight y squared plus 7 straight y plus 2 close square brackets end fraction equals integral fraction numerator dy over denominator open square brackets 6 straight y squared plus 7 straight y plus 2 close square brackets end fraction equals integral fraction numerator dy over denominator open parentheses 3 straight y plus 2 close parentheses open parentheses 2 straight y plus 1 close parentheses end fraction
rightwards double arrow straight I equals integral open square brackets fraction numerator 2 over denominator 2 straight y plus 1 end fraction minus fraction numerator 3 over denominator 3 straight y plus 2 end fraction close square brackets dy equals integral fraction numerator 2 over denominator 2 straight y plus 1 end fraction dy minus integral fraction numerator 3 over denominator 3 straight y plus 2 end fraction dy
rightwards double arrow straight I equals log open parentheses 2 straight y plus 1 close parentheses minus log open parentheses 3 straight y plus 2 close parentheses
rightwards double arrow straight I equals log open parentheses 2 logx plus 1 close parentheses minus log open parentheses 3 logx plus 2 close parentheses
Hence comma space integral fraction numerator dx over denominator straight x open square brackets 6 open parentheses logx close parentheses squared plus 7 logx plus 2 close square brackets end fraction equals log open parentheses 2 logx plus 1 close parentheses minus log open parentheses 3 logx plus 2 close parentheses equals log open parentheses fraction numerator 2 logx plus 1 over denominator 3 logx plus 2 end fraction close parentheses](https://images.topperlearning.com/topper/tinymce/cache/2a21cea0c99e7fe7958c71026de4c3ca.png)
Answered by Renu Varma | 05 Oct, 2020, 10:55: AM
Concept Videos
CBSE 12-science - Maths
Asked by aalavarshitha2005 | 21 Jan, 2024, 17:28: PM
CBSE 12-science - Maths
Asked by atharvaparkar04 | 17 Dec, 2023, 12:59: PM
CBSE 12-science - Maths
Asked by shashinayaka032 | 05 Dec, 2023, 12:46: PM
CBSE 12-science - Maths
Asked by manasvichandel49 | 19 Oct, 2023, 08:53: AM
CBSE 12-science - Maths
Asked by diptiranigupta1981 | 02 Oct, 2023, 18:33: PM
CBSE 12-science - Maths
Asked by sdmbotch1123 | 30 Sep, 2023, 22:54: PM
CBSE 12-science - Maths
Asked by sdmbotch1123 | 16 Jan, 2023, 20:18: PM
CBSE 12-science - Maths
Asked by devilkano80 | 07 Jul, 2022, 13:45: PM