Question

Evaluate : $\int \frac{1}{\sqrt{2x^2+3x-2}}$dx

Answer 1

$\int \frac{dx}{\sqrt{2x^2+3x+2}}=\int \frac{dx}{\sqrt{2[{(x+\frac{3}{4})}^2-\frac{25}{16}]}}=\frac{1}{\sqrt{2}}\int \frac{dx}{[{(x+\frac{3}{4})}^2-{\left(\frac{5}{4}\right)}^2]}=\frac{1}{\sqrt{2}}\ln |x+{(x+\frac{3}{4})}^2-{\left(\frac{5}{4}\right)}^2|+C$