calculate-1-2-1-dx-4x-2-1-4x-2-1-

Question Number 66339 by mathmax by abdo last updated on 12/Aug/19

c a l c u l a t e \int_{\frac{1}{2}}^{1} \frac{d x}{\sqrt{4 x^{2} - 1} + \sqrt{4 x^{2} + 1}}

Commented by Prithwish sen last updated on 13/Aug/19

\frac{1}{2} \int_{\frac{1}{2}}^{1} [\sqrt{{4 x}^{2} + 1} - \sqrt{{4 x}^{2} - 1]} dx

= \frac{1}{4} {[x \sqrt{{4 x}^{2} + 1} + \frac{1}{2} \ln ∣ 2 x + \sqrt{{4 x}^{2} + 1} ∣ - x \sqrt{{4 x}^{2} - 1} + \frac{1}{2} \ln ∣ 2 x + \sqrt{{4 x}^{2} - 1} ∣]}_{\frac{1}{2}}^{1}