If d x x²⁰²² (1+x²⁰²² )^ 1 / 2022 = - (1+x^m )^ n / m n x^n +C , then m - n =

Step-by-step solution

Given dx x ²⁰²² (1+ x ²⁰²² )^ 1 / 2002 dx x ²⁰²³ (1+ x ⁻²⁰²² )^ 1 / 2022 Let 1+ x ⁻²⁰²²= t -2022 x ⁻²⁰⁰³ dx = dt or dx x ²⁰²³ = -1 2022 dt aligned & = - dt 2002 ( t ) 1 2022 & = -1 2022 t ^ -1 2002 dt aligned aligned & -1 2022 t ^ -1 2022 +1 -1 2022 +1 & -1 2022 (1+ x ²⁰⁰² )^ 2001 2022 2021 2022 aligned -1 2022 (1+ x ²⁰⁰² )^ 2001 2022 2021 2022 (1+x²⁰²² )^ 2021 2002 ²⁰²¹ x²⁰²¹ +c m =2022 and n =2021 m - n =1