Question-40952

Question Number 40952 by Raj Singh last updated on 30/Jul/18

Commented by abdo mathsup 649 cc last updated on 30/Jul/18

l e t I = \int \frac{d x}{{(9 - x^{2})}^{\frac{3}{2}}}

I =_{x = 3 s i n θ} \int \frac{3 c o s θ d θ}{9^{\frac{3}{2}} {(1 - {s i n}^{2} θ)}^{\frac{3}{2}}}

= \frac{1}{9} \int \frac{c o s θ}{{c o s}^{3} θ} d θ = \frac{1}{9} \int \frac{d θ}{{c o s}^{2} θ}

9 I = \int (1 + {t a n}^{2} θ) d θ =_{t a n θ = u} \int (1 + u^{2}) \frac{d u}{1 + u^{2}}

= u + c = t a n θ + c = t a n (a r c s i n (\frac{x}{3})) + c

I = \frac{1}{9} t a n (a r c s i n (\frac{x}{3})) + c .