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Aus Online Mathematik Brückenkurs 2

If we recall that x=x12 , the integral can be written as

94x−1xdx=94x12−1x12dx=94x12−x−12dx

This is a standard integral in which the integrand consists of two terms looking like xn, where n=21 and n=−21.

We obtain

94x12−x−12dx=x21+121+1−x−21+1−21+194=23x1+21−21x2194=32xx−2x94=3299−29−3244−24=3293−23−3242−22=18−6−316+4=16−316=3163−16=332