Sr Examen
Integral de ln((x^2+5)/(x^2+2)) dx
Solución
Ha introducido
[src]
oo / | | / 2 \ | |x + 5| | log|------| dx | | 2 | | \x + 2/ | / 1
$$\int\limits_{1}^{\infty} \log{\left(\frac{x^{2} + 5}{x^{2} + 2} \right)}\, dx$$
Integral(log((x^2 + 5)/(x^2 + 2)), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | / 2 \ / 2 \ / ___\ / ___\ | |x + 5| |x + 5| ___ |x*\/ 2 | ___ |x*\/ 5 | | log|------| dx = C + x*log|------| - 2*\/ 2 *atan|-------| + 2*\/ 5 *atan|-------| | | 2 | | 2 | \ 2 / \ 5 / | \x + 2/ \x + 2/ | /
$$\int \log{\left(\frac{x^{2} + 5}{x^{2} + 2} \right)}\, dx = C + x \log{\left(\frac{x^{2} + 5}{x^{2} + 2} \right)} - 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} \right)}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ ___ ___ |\/ 5 | ___ |\/ 2 |
-log(2) + pi*\/ 5 - pi*\/ 2 - 2*\/ 5 *atan|-----| + 2*\/ 2 *atan|-----|
\ 5 / \ 2 /
$$- \sqrt{2} \pi - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} \right)} - \log{\left(2 \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + \sqrt{5} \pi$$
=
=
/ ___\ / ___\
___ ___ ___ |\/ 5 | ___ |\/ 2 |
-log(2) + pi*\/ 5 - pi*\/ 2 - 2*\/ 5 *atan|-----| + 2*\/ 2 *atan|-----|
\ 5 / \ 2 /
$$- \sqrt{2} \pi - 2 \sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} \right)} - \log{\left(2 \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + \sqrt{5} \pi$$
-log(2) + pi*sqrt(5) - pi*sqrt(2) - 2*sqrt(5)*atan(sqrt(5)/5) + 2*sqrt(2)*atan(sqrt(2)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.