Sr Examen
Integral de ln(x+(x^2-0,25)^(1/2))/(2*x^2) dx
Solución
Ha introducido
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17 -- 10 / | | / ________\ | | / 2 1 | | log|x + / x - - | | \ \/ 4 / | --------------------- dx | 2 | 2*x | / 1/2
$$\int\limits_{\frac{1}{2}}^{\frac{17}{10}} \frac{\log{\left(x + \sqrt{x^{2} - \frac{1}{4}} \right)}}{2 x^{2}}\, dx$$
Integral(log(x + sqrt(x^2 - 1/4))/((2*x^2)), (x, 1/2, 17/10))
Respuesta (Indefinida)
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/
|
| / ________\ / ________\ /
| | / 2 1 | / | / 2 1 | |
| log|x + / x - - | | log|x + / x - - | | ______________________
| \ \/ 4 / | x \ \/ 4 / | \/ (1 + 2*x)*(-1 + 2*x)
| --------------------- dx = C + 2* | ------------------------------- dx - --------------------- + | ---------------------------------- dx
| 2 | ___________ 2*x | / ___________\
| 2*x | 3 2 / 2 | | 2 / 2 |
| | -x + 4*x + 2*x *\/ -1 + 4*x | x*\-1 + 4*x + 2*x*\/ -1 + 4*x /
/ | |
/ /
$$\int \frac{\log{\left(x + \sqrt{x^{2} - \frac{1}{4}} \right)}}{2 x^{2}}\, dx = C + 2 \int \frac{x}{4 x^{3} + 2 x^{2} \sqrt{4 x^{2} - 1} - x}\, dx + \int \frac{\sqrt{\left(2 x - 1\right) \left(2 x + 1\right)}}{x \left(4 x^{2} + 2 x \sqrt{4 x^{2} - 1} - 1\right)}\, dx - \frac{\log{\left(x + \sqrt{x^{2} - \frac{1}{4}} \right)}}{2 x}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.