cosec ^2 x-2022 ²⁰²² x d x=f(x)+C f( / 4)=

Step-by-step solution

I= cosec ^2 x-2022 ²⁰²² x d x aligned & = ( x)⁻²⁰²² cosec ^2 x d x-2022 d x ²⁰²² x & =( x)⁻²⁰²² cosec ^2 x d x aligned array r . .- [-2022)( x)⁻²⁰²³(- x) ] cosec ^2 x d x ] d x -2022 d x ²⁰²² x array aligned & =( x)⁻²⁰²² (- x)-2022 & ( x)⁻²⁰²²( x)(- x) d x-2022 d x ²⁰²² x aligned aligned & = - x ( x)²⁰²² +2022 d x ( x)²⁰²² -2022 & d x ( x)²⁰²² +C= - x ( x)²⁰²² +C aligned aligned & f(x)= - x ( x)²⁰²² & ( 4 )= -1 (1 / 2 )²⁰²² =-2¹⁰¹¹ aligned