I=∫4x+1√(2x^2+x 3)dx Let 2x^2+x 3=t Differentiating, (4x+1)dx=dt ∴ I=∫dt√(t) =2t^1/2 =2 (2x^2+x 3)^1/2 ...

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Integration of Irrational Algebraic Fractions - 1

Solve I=∫4x...

Question

Solve $I = \int \frac{4 x + 1}{\sqrt{2 x^{2} + x - 3}}$

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Solution

$I = \int \frac{4 x + 1}{\sqrt{2 x^{2} + x - 3}} d x$
Let $2 x^{2} + x - 3 = t$
Differentiating, $(4 x + 1) d x = d t$
$∴ I = \int \frac{d t}{\sqrt{t}}$
$= 2 t^{1 / 2}$
$= 2 (2 x^{2} + x - 3)^{1 / 2}$

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