∫ 1 √ 16 − 6 X − X 2 D X - Mathematics

Question

\int \frac{1}{\sqrt{16 - 6 x - x^{2}}} d x

Sum

Solution

$\int \frac{d x}{\sqrt{16 - 6 x - x^{2}}}$
$= \int \frac{d x}{\sqrt{16 - (x^{2} + 6 x)}}$
$= \int \frac{d x}{\sqrt{16 - (x^{2} + 6 x + 3^{2} - 3^{2})}}$
$= \int \frac{d x}{\sqrt{16 + 9 - {(x + 3)}^{2}}}$
$= \int \frac{d x}{\sqrt{5^{2} - {(x + 3)}^{2}}}$
$= \sin^{- 1} (\frac{x + 3}{5}) + C$

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Indefinite Integral Problems

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Q 7 Q 6 Q 8

Chapter 19: Indefinite Integrals - Exercise 19.17 [Page 93]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.17 | Q 7 | Page 93

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∫ 1 √ 16 − 6 X − X 2 D X - Mathematics

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