I am trying to calculate the integral &#x222B;<!-- ∫ --> d x </mrow>

cooloicons62

cooloicons62

Answered question

2022-07-01

I am trying to calculate the integral
d x ( x + 1 ) 2 ( x 1 ) 7 3 .

Answer & Explanation

Jordin Church

Jordin Church

Beginner2022-07-02Added 11 answers

Substitute t 3 = x + 1 x 1 . Then, x = t 3 + 1 t 3 1 , d x = 6 t 2 ( t 3 1 ) 2 d t and
1 ( x + 1 ) 2 ( x 1 ) 7 3 d x = 3 4 ( t 3 1 ) d t = 3 16 t 4 + 3 4 t + C = 3 16 ( x + 1 x 1 ) 4 3 + 3 4 ( x + 1 x 1 ) 1 3 + C = 3 16 ( 3 x 5 ) x + 1 ( x 1 ) 4 3 + C

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