Equation: ∫ y 5 y 3 − 2 d y

gorgeousgen9487

gorgeousgen9487

Answered

2022-07-07

Equation:
y 5 y 3 2   d y

Answer & Explanation

isscacabby17

isscacabby17

Expert

2022-07-08Added 13 answers

I think it's easier to make a substitution:
u = y 3 2 u 2 = y 3 2 2 u d u = 3 y 2 d y
y 5 y 3 2 d y = 1 3 y 3 y 3 2 ( 3 y 2 d y ) = 1 3 ( u 2 + 2 ) u ( 2 u d u ) = 2 3 u 4 + 2 u 2 d u = 2 3 ( u 5 5 + 2 u 3 3 ) + C = 2 15 ( y 3 2 ) 5 / 2 + 4 9 ( y 3 2 ) 3 / 2 + C
Grimanijd

Grimanijd

Expert

2022-07-09Added 4 answers

y 3 2 = x y 5 y 3 2   d y = 1 3 ( x + 2 ) x   d x .
Now,
1 3 ( x + 2 ) x   d x = 1 3 x x   d x + 1 3 2 x   d x
= 2 15 x 5 2 + 4 9 x 3 2 = 2 15 ( y 3 3 ) 5 2 + 4 9 ( y 3 3 ) 3 2 .

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