Example 9 (iii) - Class 12

Transcript

Example 9 Find the following integrals: (iii) ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥﷮2﷯ − 2𝑥﷯ ﷯﷯ ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥﷮2﷯ − 2𝑥﷯ ﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥﷮2﷯ − 2﷮5﷯𝑥﷯﷯ ﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥﷮2﷯ − 2 𝑥﷯ 1﷮5﷯﷯﷯﷯ ﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥﷮2﷯ − 2 𝑥﷯ 1﷮5﷯﷯ + 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯ ﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5 𝑥 − 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯ ﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5﷯ ﷮ 𝑥 − 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯﷯ = ﷮﷮ 𝑑𝑥﷮ ﷮5﷯ ﷮ 𝑥 − 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯﷯ = 1﷮ ﷮5﷯﷯ 𝑙𝑜𝑔 𝑥− 1﷮5﷯+ ﷮ 𝑥− 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯+𝐶1﷯ = 1﷮ ﷮5﷯﷯𝑙𝑜𝑔 𝑥− 1﷮5﷯+ ﷮ 𝑥− 1﷮5﷯﷯﷮2﷯− 1﷮5﷯﷯﷮2﷯﷯﷯+ 𝐶1﷮ ﷮5﷯﷯ = 1﷮ ﷮5﷯﷯𝑙𝑜𝑔 𝑥− 1﷮5﷯+ ﷮ 𝑥﷮2﷯+ 1﷮5﷯﷯﷮2﷯−2 𝑥﷯ 1﷮5﷯﷯− 1﷮5﷯﷯﷮2﷯﷯﷯+𝐶 = 1﷮ ﷮5﷯﷯𝑙𝑜𝑔 𝑥− 1﷮5﷯+ ﷮ 𝑥﷮2﷯− 2𝑥﷮5﷯﷯﷯+𝐶