First slide

Methods of integration

Question

$\int \frac{d x}{\sqrt{2 + x - 3 x^{2}}}$

Easy

A

$\frac{1}{\sqrt{3}} \cos^{- 1} (\frac{3 x - 1}{5}) + C$
B

$\frac{1}{\sqrt{3}} \tan^{- 1} (\frac{6 x - 1}{5}) + C$
C

$\frac{1}{\sqrt{3}} \sec^{- 1} (\frac{6 x - 1}{5}) + C$
D

$\frac{1}{\sqrt{3}} \sin^{- 1} (\frac{6 x - 1}{5}) + C$

Solution

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

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