Mathematics

Evaluate: $\displaystyle \int \sqrt{\dfrac{x - 5}{x - 9}}dx$.

SOLUTION
Let $I=$$\displaystyle \int \sqrt{\dfrac{x - 5}{x - 9}}dx. Let x-9=z^2......(1) then dx=2zdz Using these in the above expression we get, I=$$2\displaystyle \int \sqrt{z^2+4}dz$
or, $I=$$2\displaystyle \int \sqrt{z^2+2^2}dz$
or, $I=2\left(\dfrac{z\sqrt{z^2+4}}{2}+\dfrac{2^2}{2}\log|z+\sqrt{z^2+4}|\right)+c$ [ Where $c$ is integrating constant]
or, $I=\sqrt{(x-9)(x-5)}+4\log|\sqrt{x-9}+\sqrt{x-5}|+c$. [ Using (1)]

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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