Ex 7.6, 8 - Integrate x tan-1 x - Chapter 7 Class 12 NCERT

Ex 7.6, 8 𝑥 tan﷮−1﷯﷮𝑥﷯ ﷮﷮𝑥 tan﷮−1﷯﷮𝑥﷯﷯ 𝑑𝑥 ﷮﷮𝑥 tan﷮−1﷯﷮𝑥﷯﷯ 𝑑𝑥 = ﷮﷮ tan﷮−1﷯﷮𝑥﷯﷯﷯𝑥 𝑑𝑥 = tan﷮−1﷯﷮𝑥﷯ ﷮﷮𝑥﷯𝑑𝑥− ﷮﷮ 𝑑 tan﷮−1﷯﷮𝑥﷯﷯﷮𝑑𝑥﷯ ﷮﷮𝑥 .𝑑𝑥﷯﷯𝑑𝑥﷯ = tan﷮−1﷯﷮𝑥﷯. 𝑥﷮2﷯﷮2﷯ − ﷮﷮ 1﷮1 + 𝑥﷮2﷯﷯ . 𝑥﷮2﷯﷮2﷯. 𝑑𝑥﷯ = 𝑥﷮2﷯﷮2﷯ tan﷮−1﷯﷮𝑥﷯− 1﷮2﷯ ﷮﷮ 𝑥﷮2﷯﷮ 𝑥﷮2﷯ + 1﷯ 𝑑𝑥﷯ = 𝑥﷮2﷯﷮2﷯ tan﷮−1﷯﷮𝑥﷯− 1﷮2﷯ ﷮﷮ 𝑥﷮2﷯ + 1 − 1﷮ 𝑥﷮2﷯ + 1﷯ 𝑑𝑥﷯ = 𝑥﷮2﷯﷮2﷯ tan﷮−1﷯﷮𝑥﷯− 1﷮2﷯ ﷮﷮ 𝑥﷮2﷯ + 1﷮ 𝑥﷮2﷯ + 1﷯ 𝑑𝑥﷯− ﷮﷮ 𝑑𝑥﷮ 𝑥﷮2﷯ + 1﷯﷯﷯ = 𝑥﷮2﷯﷮2﷯ tan﷮−1﷯﷮𝑥﷯− 1﷮2﷯ 𝑑𝑥− ﷮﷮ 𝒅𝒙﷮ 𝒙﷮𝟐﷯ + 𝟏﷯﷯﷯ = 𝑥﷮2﷯﷮2﷯ tan﷮−1﷯﷮𝑥﷯− 1﷮2﷯𝑥+ 1﷮2﷯ × 𝟏﷮𝟏﷯ 𝐭𝐚𝐧﷮−𝟏﷯ 𝒙﷮𝟏﷯+𝐶 = 𝒙﷮𝟐﷯﷮𝟐﷯ 𝐭𝐚𝐧﷮−𝟏﷯﷮𝒙﷯− 𝒙﷮𝟐﷯+ 𝟏﷮𝟐﷯ 𝐭𝐚𝐧﷮−𝟏﷯ 𝒙+𝑪