Mathematics

# Solve:$\displaystyle\int {\dfrac{{3xdx}}{{\sqrt {1 - {x^2}} }}}$

##### SOLUTION

Consider the given integral.

$I=\displaystyle\int{\dfrac{3x}{\sqrt{1-{{x}^{2}}}}}dx$

Let $t=1-{{x}^{2}}$

$\dfrac{dt}{dx}=0-2x$

$-\dfrac{dt}{2}=xdx$

Therefore,

$I=-\dfrac{3}{2}\displaystyle\int{\dfrac{1}{\sqrt{t}}}dt$

$I=-\dfrac{3}{2}\left( 2\sqrt{t} \right)+C$

$I=-3\sqrt{t}+C$

On putting the value of $t$, we get

$I=-3\sqrt{1-{{x}^{2}}}+C$

Hence, this is the answer.

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

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