Sr Examen
Integral de (x^(3/2))/(1+x*x) dx
Solución
Ha introducido
[src]
1 / | | 3/2 | x | ------- dx | 1 + x*x | / 0
$$\int\limits_{0}^{1} \frac{x^{\frac{3}{2}}}{x x + 1}\, dx$$
Integral(x^(3/2)/(1 + x*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 3/2 ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ | x ___ \/ 2 *atan\1 + \/ 2 *\/ x / \/ 2 *atan\-1 + \/ 2 *\/ x / \/ 2 *log\4 + 4*x + 4*\/ 2 *\/ x / \/ 2 *log\4 + 4*x - 4*\/ 2 *\/ x / | ------- dx = C + 2*\/ x - --------------------------- - ---------------------------- - ---------------------------------- + ---------------------------------- | 1 + x*x 2 2 4 4 | /
$$\int \frac{x^{\frac{3}{2}}}{x x + 1}\, dx = C + 2 \sqrt{x} + \frac{\sqrt{2} \log{\left(- 4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} \sqrt{x} + 4 x + 4 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} - \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
___ ___ / ___\ ___ / ___\
pi*\/ 2 \/ 2 *log\8 + 4*\/ 2 / \/ 2 *log\8 - 4*\/ 2 /
2 - -------- - ---------------------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \pi}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + 2$$
=
=
___ ___ / ___\ ___ / ___\
pi*\/ 2 \/ 2 *log\8 + 4*\/ 2 / \/ 2 *log\8 - 4*\/ 2 /
2 - -------- - ---------------------- + ----------------------
4 4 4
$$- \frac{\sqrt{2} \pi}{4} - \frac{\sqrt{2} \log{\left(4 \sqrt{2} + 8 \right)}}{4} + \frac{\sqrt{2} \log{\left(8 - 4 \sqrt{2} \right)}}{4} + 2$$
2 - pi*sqrt(2)/4 - sqrt(2)*log(8 + 4*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.