Asked by eve
Find the integral.
x^4/the square root of (x^5-1)
x^4/the square root of (x^5-1)
Answers
Answered by
Reiny
did you notice that the derivative of x^5=1 is 4x^4 which is a multiple of x^4, so it is straightforward
integral [ x4/(√(x^5 - 1)^(1/2)
= int [ x^4 (x^5 - 1)^(-1/2)
= (2/5) (x^5 - 1)^(1/2) + c
check by taking the derivative, it works
integral [ x4/(√(x^5 - 1)^(1/2)
= int [ x^4 (x^5 - 1)^(-1/2)
= (2/5) (x^5 - 1)^(1/2) + c
check by taking the derivative, it works
Answered by
sani
correctin: the derivative of x^5=1 is 5x^4
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