Ask a Doubt

Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Integration x . log(x + 1) dx explain in great detail and give full solution

Asked by haroonrashidgkp | 18 Oct, 2018, 04:30: PM

Expert Answer

u s e space L I A T E left parenthesis log a r i t h m comma i n v e r s e comma a l g e b r a i c comma t r i g n o m e t r y comma e x p o n e n t i a l right parenthesis a c c o r d i n g l y space d e c i d e space u space a n d space v. i n space o u r space c a s e space x. log left parenthesis x plus 1 right parenthesis space s o space b y space L I A T E space t a k e space u equals log left parenthesis x plus 1 right parenthesis space a n d space v equals x. s o space i n t e g r a t i o n space b y space p a r t s integral u v space d x equals u integral v d x minus integral left square bracket fraction numerator d u over denominator d x end fraction integral v d x right square bracket d x integral log left parenthesis x plus 1 right parenthesis x d x equals log left parenthesis x plus 1 right parenthesis integral x d x minus integral left square bracket fraction numerator d log left parenthesis x plus 1 right parenthesis over denominator d x end fraction integral x d x right square bracket d x equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus integral fraction numerator 1 over denominator x plus 1 end fraction. x squared over 2 space d x equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus 1 half integral fraction numerator x squared over denominator x plus 1 end fraction. space d x n o w space root index x plus 1 of x squared end root space comma i. e space d i v i d e space x squared space b y space x plus 1 w e space g e t space x squared equals left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus 1 equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus 1 half integral fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus 1 over denominator x plus 1 end fraction. space d x equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus 1 half integral fraction numerator left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis over denominator x plus 1 end fraction plus fraction numerator 1 over denominator x plus 1 end fraction. space d x equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus 1 half integral x minus 1 plus fraction numerator 1 over denominator x plus 1 end fraction. space d x equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus 1 half left square bracket x squared over 2 minus x plus log vertical line x plus 1 vertical line right square bracket plus space c equals log left parenthesis x plus 1 right parenthesis space x squared over 2 minus x squared over 4 plus x over 2 minus 1 half log vertical line x plus 1 vertical line right square bracket plus space c

Answered by Ram Singh | 18 Oct, 2018, 07:50: PM

Concept Videos

Practice Test

Webinar

Pre Board Assessment

Answered Unanswered My Questions My Answers

CBSE 12-science - Maths

Ans is 1/2 but I need the stepwise solution

Asked by dattashibani456 | 06 Apr, 2022, 01:07: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

`I=int x cos^(-1)xdx`

Asked by sujachris1969 | 08 Jul, 2020, 04:47: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Pl ans as fast as possible

Asked by jain.pradeep | 10 Jan, 2020, 10:21: AM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integrate. x arcsinx dx

Asked by Harsh | 25 Jul, 2019, 07:02: AM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integration ( sin^-1 (x)^1/2 – cos^-1 (x)^1/2/sin^-1 (x)^1/2 + cos^-1 (x)^1/2) dx

Asked by haroonrashidgkp | 29 Oct, 2018, 12:05: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integration ( sin^-1 (x)^1/2 – cos^-1 (x)^1/2/sin^-1 (x)^1/2 + cos^-1 (x)^1/2) dx

Asked by haroonrashidgkp | 28 Oct, 2018, 01:19: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integration 2 x³ e^{x square} dx explain in great detail and give full solution

Asked by haroonrashidgkp | 18 Oct, 2018, 04:31: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integration x . log(x + 1) dx explain in great detail and give full solution

Asked by haroonrashidgkp | 18 Oct, 2018, 04:30: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integration x² cos³ x dx explain in great detail and give full solution

Asked by haroonrashidgkp | 18 Oct, 2018, 04:30: PM

ANSWERED BY EXPERT

CBSE 12-science - Maths

Integrate:

Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM

ANSWERED BY EXPERT

My Class Videos Tests Plans Ask a Doubt