∫ 1 √ 7 − 6 X − X 2 D X - Mathematics

Sum
$\int\frac{1}{\sqrt{7 - 6x - x^2}} dx$

Solution

$\int\frac{dx}{\sqrt{7 - 6x - x^2}}$
$= \int\frac{dx}{\sqrt{7 - \left( x^2 + 6x \right)}}$
$= \int\frac{dx}{\sqrt{7 - \left[ x^2 + 6x + 3^2 - 3^2 \right]}}$
$= \int\frac{dx}{\sqrt{7 + 9 - \left( x + 3 \right)^2}}$
$= \int\frac{dx}{\sqrt{4^2 - \left( x + 3 \right)^2}}$
$= \sin^{- 1} \left( \frac{x + 3}{4} \right) + C$

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.17 | Q 8 | Page 93