Integrate the function. int (x cos^(−1)x)(sqrt(1−x^2))dx.

Chanel Hunter

Chanel Hunter

Answered question

2023-02-26

Integrate the function. x cos 1 x 1 x 2 d x

Answer & Explanation

Marin Valencia

Marin Valencia

Beginner2023-02-27Added 10 answers

Let I = x cos 1 x 1 x 2 d x I = cos 1 x x 1 x 2 d x
Consider cos 1 x as first function and x 1 x 2 as a second function and integration the components, we obtain
I = cos 1 x x 1 x 2 d x [ d d x ( cos 1 x ) x 1 x 2 d x ] d x Let  1 x 2 = t 2 2 x = 2 t d t d x d x = t x d t I = cos 1 x x t ( t x ) d t [ d d x ( cos 1 x ) x t ( t x ) d t ] d x = cos 1 x ( t ) [ ( 1 ) 1 x 2 ( t ) d t ] d x [ 1 x 2 = t 2 t = 1 x 2 ] = 1 x 2 cos 1 x 1 d x = 1 x 2 cos 1 x x + C

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