Check sibling questions

Example 23 - Find integral root x2 + 2x + 5 dx - Examples

Example 23 - Chapter 7 Class 12 Integrals - Part 2

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Transcript

Example 23 Find ﷐﷮﷮﷐﷮﷐𝑥﷮2﷯+2𝑥+5﷯﷯ 𝑑𝑥 ﷐﷮﷮﷐﷮﷐𝑥﷮2﷯+2𝑥+5﷯﷯ 𝑑𝑥 = ﷐﷮﷮﷐﷮﷐𝑥﷮2﷯+2𝑥+1+4﷯﷯ 𝑑𝑥 = ﷐﷮﷮﷐﷮﷐(𝑥+1)﷮2﷯+4﷯﷯ 𝑑𝑥 Let y = x + 1 ﷐𝑑𝑦 ﷮𝑑𝑥﷯=1 dy = dx Substituting = ﷐﷮﷮﷐﷮﷐𝑦﷮2﷯+4﷯﷯ 𝑑𝑦 = ﷐﷮﷮﷐﷮﷐𝑦﷮2﷯+﷐(2)﷮2﷯﷯﷯ 𝑑𝑦 = ﷐𝑦﷮2﷯ ﷐﷮﷐𝑦﷮2﷯+4﷯+ ﷐4﷮2﷯﷐ log﷮﷐𝑦+﷐﷮﷐𝑦﷮2﷯+4﷯﷯﷯+ C = ﷐𝑦﷮2﷯﷐﷮﷐𝑦﷮2﷯+4﷯+2 𝑙𝑜𝑔﷐𝑦+﷐﷮﷐𝑦﷮2﷯+4﷯﷯+ C Putting value of y = x + 1 = ﷐𝑥 + 1﷮2﷯ ﷐﷮﷐(𝑥+1)﷮2﷯ + 4﷯+2 𝑙𝑜𝑔﷐𝑥+1+﷐﷮﷐(𝑥+1)﷮2﷯ + 4﷯﷯+ C = ﷐𝑥 + 1﷮2﷯﷐﷮﷐𝑥﷮2﷯+1+2𝑥+ 4﷯+2 𝑙𝑜𝑔﷐𝑥+1+﷐﷮﷐𝑥﷮2﷯+1+2𝑥+ 4﷯﷯+ C = ﷐𝟏﷮𝟐﷯ (x + 1) ﷐﷮﷐𝒙﷮𝟐﷯ 𝟐𝒙+𝟓﷯+𝟐﷐𝐥𝐨𝐠﷮﷐𝒙+𝟏+﷐﷮﷐𝒙﷮𝟐﷯+𝟐𝒙+𝟓﷯﷯﷯+𝐂

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.