`int_(-1)^1 5x^4 sqrt(x^5 +1) dx `

Explanation

यहाँ `underset(-1)overset(1)int 5x^(4) sqrt(x^(5)+1)dx`
माना `x^(5)+1=t rArr 5x^(4)dx=dt`
जब `x=-1 rArr t=(1)^(5)+1=2`
`therefore I=underset(0)overset(2)int sqrtt dt=2/3 [t^(3//2)]_(0)^(2)`
`=2/3[2sqrt2-0]=(4sqrt2)/3`