Mathematics

# Solve :$\displaystyle \int x \sqrt{x^2-1 dx}$

##### SOLUTION
$=\displaystyle \int x\sqrt {x^2 -1}dx$
Let $x^2-1=t_1\ 2x\ dx=dt$
$\boxed {x\ dx=\dfrac {dt}{2}}$
$=\dfrac {1}{2}\displaystyle \int \sqrt {t} dt$
$=\dfrac {1}{2}\ \dfrac {t^{3/2}}{3/2}+C$
$=\dfrac {1}{2}.\dfrac {2}{3} (x^2-1)^{3/2}+C$
$=\dfrac {(x^2 -1)}{3}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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