Sr Examen
Integral de (x^1/2)/(x^2+1) dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ x | ------ dx | 2 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{x^{2} + 1}\, dx$$
Integral(sqrt(x)/(x^2 + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | ___ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ | \/ x \/ 2 *atan\1 + \/ 2 *\/ x / \/ 2 *atan\-1 + \/ 2 *\/ x / \/ 2 *log\1 + x + \/ 2 *\/ x / \/ 2 *log\1 + x - \/ 2 *\/ x / | ------ dx = C + --------------------------- + ---------------------------- - ------------------------------ + ------------------------------ | 2 2 2 4 4 | x + 1 | /
$$\int \frac{\sqrt{x}}{x^{2} + 1}\, dx = C + \frac{\sqrt{2} \log{\left(- \sqrt{2} \sqrt{x} + x + 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(\sqrt{2} \sqrt{x} + x + 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
___ / ___\ ___ ___ / ___\
\/ 2 *log\8 + 4*\/ 2 / pi*\/ 2 \/ 2 *log\8 - 4*\/ 2 /
- ---------------------- + -------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \pi}{4}$$
=
=
___ / ___\ ___ ___ / ___\
\/ 2 *log\8 + 4*\/ 2 / pi*\/ 2 \/ 2 *log\8 - 4*\/ 2 /
- ---------------------- + -------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \pi}{4}$$
-sqrt(2)*log(8 + 4*sqrt(2))/4 + pi*sqrt(2)/4 + sqrt(2)*log(8 - 4*sqrt(2))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.