Sr Examen
Integral de ln((x^2+3)/(x^2+2))dx dx
Solución
Ha introducido
[src]
oo / | | / 2 \ | |x + 3| | log|------| dx | | 2 | | \x + 2/ | / 1
$$\int\limits_{1}^{\infty} \log{\left(\frac{x^{2} + 3}{x^{2} + 2} \right)}\, dx$$
Integral(log((x^2 + 3)/(x^2 + 2)), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | / 2 \ / 2 \ / ___\ / ___\ | |x + 3| |x + 3| ___ |x*\/ 2 | ___ |x*\/ 3 | | log|------| dx = C + x*log|------| - 2*\/ 2 *atan|-------| + 2*\/ 3 *atan|-------| | | 2 | | 2 | \ 2 / \ 3 / | \x + 2/ \x + 2/ | /
$$\int \log{\left(\frac{x^{2} + 3}{x^{2} + 2} \right)}\, dx = C + x \log{\left(\frac{x^{2} + 3}{x^{2} + 2} \right)} - 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} \right)} + 2 \sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} x}{3} \right)}$$
Gráfica
Respuesta
[src]
/ ___\ ___
___ ___ |\/ 2 | 2*pi*\/ 3
-log(4/3) - pi*\/ 2 + 2*\/ 2 *atan|-----| + ----------
\ 2 / 3
$$- \sqrt{2} \pi - \log{\left(\frac{4}{3} \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + \frac{2 \sqrt{3} \pi}{3}$$
=
=
/ ___\ ___
___ ___ |\/ 2 | 2*pi*\/ 3
-log(4/3) - pi*\/ 2 + 2*\/ 2 *atan|-----| + ----------
\ 2 / 3
$$- \sqrt{2} \pi - \log{\left(\frac{4}{3} \right)} + 2 \sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)} + \frac{2 \sqrt{3} \pi}{3}$$
-log(4/3) - pi*sqrt(2) + 2*sqrt(2)*atan(sqrt(2)/2) + 2*pi*sqrt(3)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.