_ ^ x^2 - 8x + 7 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\sqrt {{x^2} - 8x + 7} } \;dx = $

A
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} + 9\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
B
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - 3\sqrt 2 \log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
✓
$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - \frac{9}{2}\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$
D
None of these

✓

Answer

Correct option: C.

$\frac{1}{2}(x - 4)\sqrt {{x^2} - 8x + 7} - \frac{9}{2}\log [x - 4 + \sqrt {{x^2} - 8x + 7} ] + c$

c
(c)$\int_{}^{} {\sqrt {{x^2} - 8x + 7} \,dx = \int_{}^{} {\sqrt {{{(x - 4)}^2} - {{(3)}^2}} \,dx} } $
Now apply formula of $\int_{}^{} {\sqrt {{x^2} - {a^2}} \,dx.} $

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