Evaluate ∫ dx/(√(3 + 2x - x^2)).

Question 58

HardOriginal question

Evaluate $\int \frac{dx}{\sqrt{3 + 2x - x^{2}}}$ .

\sin^{-1}\frac{x - 1}{2} + C

Correct answerYour answer

\sin^{-1}\frac{x + 1}{2} + C

Correct answerYour answer

\frac{1}{2}\sin^{-1}\frac{x - 1}{2} + C

Correct answerYour answer

\sin^{-1}(x - 1) + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Worth noting

$\frac{1}{2}$ in front belongs to $\int \frac{dx}{x^{2} + a^{2}}$ ; $\int \frac{dx}{\sqrt{a^{2} - u^{2}}} = \sin^{-1}\frac{u}{a}$ has no such factor.

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