Integration by specific formulaes - Formula 7

Chapter 7 Class 12 Integrals
Concept wise

### Transcript

Ex 7.7, 8 β(π₯2+3π₯) β«1βγβ(π₯^2+3π₯) ππ₯γ =β«1βγβ(π₯^2+2(3/2)(π₯) ) ππ₯γ =β«1βγβ(π₯^2+2(3/2)(π₯)+(3/2)^2β(3/2)^2 ) ππ₯γ =β«1βγβ((π₯+3/2)^2β(3/2)^2 ) ππ₯γ It is of the form β«1βγβ(π₯^2βπ^2 ) ππ₯=π₯/2 β(π₯^2βπ^2 )βπ^2/2 πππ|π₯+β(π₯^2βπ^2 )|+πΆγ β΄ Replacing π₯ by π₯+3/2 and a by 3/2 , we get =(π₯ + 3/2)/2 β((π₯+3/2)^2β(3/2)^2 )β|π₯+3/2+β((π₯+π₯/2)^2β(3/2)^2 )|+πΆ =(2π₯ + 3)/4 β((π₯+3/2)^2β9/4) β 9/8 πππ|π₯+3/2 β((π₯+3/2)^2β9/4)|+πΆ =(2π₯ + 3)/4 β(π₯^2+9/4+2(π₯)(3/2)β9/4) β 9/8 πππ|π₯+3/2+β(π₯^2+9/4+2 (π₯)(3/2)β9/4)|+πΆ =(2π₯ + 3)/4 β(π₯^2+2π₯(3/2) )β 9/8 πππ|π₯+3/2+β(π₯^2+2π₯(3/2) )|+πΆ =(ππ + π)/π β(π^π+ππ)β π/π πππ|π+π/π+β(π^π+ππ)|+πͺ

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.