Question

Question #9ae03

Answer 1

`5/8(root5(y^4-8))^8+C.`.

Explanation:

We will use the Substitution `: root5(y^4-8)=x`.

`rArr (y^4-8)=x^5 rArr d(y^4-8)=d(x^5), i.e., 4y^3dy=5x^4dx`.

`"Therefore, "I=int(root5(y^4-8))^3(4y^3dy)`

`=int(x^3)(5x^4)dx=5intx^7dx=5(x^(7+1)/(7+1))=5/8x^8`.

`rArr I=5/8(root5(y^4-8))^8+C.`.