Examples

Chapter 7 Class 12 Integrals
Serial order wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Example 12 Find ﷮﷮ 𝑥﷮2﷯+ 1﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯﷯ 𝑑𝑥 Solving Integrand 𝑥﷮2﷯+ 1﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ 𝑥﷮2﷯+ 1﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯= 𝑥﷮2﷯+ 1 − 5𝑥 + 6 + 5𝑥 − 6﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ = 𝑥﷮2﷯ − 5𝑥 + 6﷯ + 5𝑥 − 5﷯﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ = 𝑥﷮2﷯ − 5𝑥 + 6﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ + 5𝑥 − 5﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ =1+ 5𝑥 − 5﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯ =1+ 5𝑥 − 5﷮ 𝑥﷮2﷯ − 2𝑥 − 3𝑥 + 6﷯ =1+ 5𝑥 − 5﷮𝑥 𝑥 − 2﷯ −3 𝑥 − 2﷯﷯ =1+ 5𝑥 − 5﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯ Now solving 5𝑥 − 5﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯ using partial fractions Let 5 𝑥 − 1﷯﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯= 𝐴﷮ 𝑥 − 2﷯﷯ + 𝐵﷮ 𝑥 − 3﷯﷯ 5 𝑥 − 1﷯﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯= 𝐴 𝑥 − 3﷯ + 𝐵 𝑥 − 2﷯﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯ ⇒5 𝑥−1﷯=𝐴 𝑥−3﷯+𝐵 𝑥−2﷯ Hence we can write it as 5 𝑥 − 1﷯﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯ = 𝐴﷮ 𝑥 − 2﷯﷯ + 𝐵﷮ 𝑥 − 3﷯﷯ Now, ﷮﷮ 𝑥﷮2﷯+ 1﷮ 𝑥﷮2﷯ − 5𝑥 + 6﷯﷯ 𝑑𝑥= ﷮﷮ 1+ 5 𝑥 − 1﷯﷮ 𝑥 − 2﷯ 𝑥 − 3﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮1+ −5﷮ 𝑥 − 2﷯﷯ + 10﷮ 𝑥 − 3﷯﷯﷯ 𝑑𝑥 = ﷮﷮1﷯𝑑𝑥− ﷮﷮ −5﷮ 𝑥 − 2﷯﷯﷯ 𝑑𝑥+ ﷮﷮ 10﷮ 𝑥 − 3﷯﷯﷯ 𝑑𝑥 =𝒙−𝟓 𝒍𝒐𝒈﷮ 𝒙−𝟐﷯﷯+𝟏𝟎 𝒍𝒐𝒈﷮ 𝒙−𝟑﷯﷯+𝐂

Made by

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.