JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \frac{\mathrm{d} x}{\sqrt{2-3 x-x^2}}=f o g(x)+C

then

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Correct option: C

f(x)=\sin ^{-1} x, g(x)=\frac{2 x+3}{\sqrt{17}}

Option C (

f(x)=\sin ^{-1} x, g(x)=\frac{{2 x+3}}{{\sqrt{{17}}}}

) is correct because completing the square and using the substitution

u = \frac{{2x+3}}{{\sqrt{{17}}}}

leads to the arcsine integral.

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