#10; #10;Let, #10; #10; #160; y=∫x 5x 7dx #10; #10; #160; y=∫x 5 2+2x 7dx #10; #10; #160; y=∫x 7+2x 7dx #10; #10; ...

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Integration by Substitution

∫√x - 5x - 7d...

Question

$\int \sqrt{\frac{x - 5}{x - 7} d x}$

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Solution

Let,

$y = \int \frac{x - 5}{x - 7} d x$

$y = \int \frac{x - 5 - 2 + 2}{x - 7} d x$

$y = \int \frac{x - 7 + 2}{x - 7} d x$

$y = \int (\frac{x - 7}{x - 7} + \frac{2}{x - 7}) d x$

$y = \int \frac{x - 7}{x - 7} d x + \int \frac{2}{x - 7} d x$

$= \int 1 d x + 2 \int \frac{1}{x - 7} d x$

$= x + 2 log x + C$

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\int \sqrt{\frac{x - 5}{x - 7}} d x = A \sqrt{x^{2} - 12 x + 35} + log | x - 6 + \sqrt{x^{2} - 12 x + 35} | + C

A =

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