Sr Examen
Integral de ln((x^2+2)/(x^2+1)) dx
Solución
Ha introducido
[src]
oo / | | / 2 \ | |x + 2| | log|------| dx | | 2 | | \x + 1/ | / 1
$$\int\limits_{1}^{\infty} \log{\left(\frac{x^{2} + 2}{x^{2} + 1} \right)}\, dx$$
Integral(log((x^2 + 2)/(x^2 + 1)), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | / 2 \ / 2 \ / ___\ | |x + 2| |x + 2| ___ |x*\/ 2 | | log|------| dx = C - 2*atan(x) + x*log|------| + 2*\/ 2 *atan|-------| | | 2 | | 2 | \ 2 / | \x + 1/ \x + 1/ | /
$$\int \log{\left(\frac{x^{2} + 2}{x^{2} + 1} \right)}\, dx = C + x \log{\left(\frac{x^{2} + 2}{x^{2} + 1} \right)} - 2 \operatorname{atan}{\left(x \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)}$$
Gráfica
Respuesta
[src]
/ ___\
pi ___ ___ |\/ 2 |
-log(3/2) - -- + pi*\/ 2 - 2*\/ 2 *atan|-----|
2 \ 2 /
$$- 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} - \frac{\pi}{2} - \log{\left(\frac{3}{2} \right)} + \sqrt{2} \pi$$
=
=
/ ___\
pi ___ ___ |\/ 2 |
-log(3/2) - -- + pi*\/ 2 - 2*\/ 2 *atan|-----|
2 \ 2 /
$$- 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} - \frac{\pi}{2} - \log{\left(\frac{3}{2} \right)} + \sqrt{2} \pi$$
-log(3/2) - pi/2 + pi*sqrt(2) - 2*sqrt(2)*atan(sqrt(2)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.