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# How to evaluate the integral of f(x)=(5x-2)^-5/2.

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College Freshman

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How to evaluate the integral of f(x)=(5x-2)^-5/2.

Posted by ulichh on April 27, 2011 at 12:32 AM via web and tagged with calculus, math

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We'll use substitution technique to evaluate the integral.

We'll put 5x - 2 = t.

We'll differentiate both sides:

5dx = dt => dx = dt/5

We'll use the negative power property:

(5x - 2)^(-5/2) = 1/(5x - 2)^(5/2)

We'll re-write the integral in t:

Int dx/(5x - 2)^(5/2) = Int dt/5*t^(5/2)

Int dt/5*t^(5/2)= (1/5)*Int t^(-5/2)dt

(1/5)*Int t^(-5/2)dt = (1/5)*t^(-5/2 + 1)/(-5/2 + 1) + C

(1/5)*Int t^(-5/2)dt = t^(-3/2)/(15/2) + C

The indefinite integral is: Int dx/(5x - 2)^(5/2) = 2/[15*(5x - 2)*sqrt(5x - 2)] + C

Posted by giorgiana1976 on April 27, 2011 at 12:38 AM (Answer #1)

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