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in Indefinite Integral by (55.0k points)
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\(\int\frac{dx}{\sqrt{1+2x-3x^2}}\) = ?

∫dx/√{1 + 2x - 3x2}

A.\(\frac{1}{\sqrt3}\)sin-1\((\frac{3x-1}2)\) + c

B.\(\frac{1}{\sqrt2}\)sin-1\((\frac{2x-1}3)\) + c

C. \(\frac{1}{\sqrt3}\)sin-1\((\frac{2x-1}3)\) + c

D. none of these

1 Answer

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Best answer

\(\int\frac{dx}{\sqrt{1+2x-3x^2}}\) = \(\int\frac{dx}{{\sqrt3}{\sqrt{-x^2+\frac{2}3x+\frac{1}3}}}\)

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