Sr Examen
Integral de (sqrt(2x))/(1+2x)^2 dx
Solución
Ha introducido
[src]
oo / | | _____ | \/ 2*x | ---------- dx | 2 | (1 + 2*x) | / 1
$$\int\limits_{1}^{\infty} \frac{\sqrt{2 x}}{\left(2 x + 1\right)^{2}}\, dx$$
Integral(sqrt(2*x)/(1 + 2*x)^2, (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / / / ___ ___\ ___ ___\\ | | ___ |atan\\/ 2 *\/ x / \/ 2 *\/ x || | _____ | ___ / ___ ___\ \/ 2 *|----------------- + -----------|| | \/ 2*x ___ |\/ 2 *atan\\/ 2 *\/ x / \ 2 2*(1 + 2*x)/| | ---------- dx = C + \/ 2 *|----------------------- - ---------------------------------------| | 2 \ 2 2 / | (1 + 2*x) | /
$$\int \frac{\sqrt{2 x}}{\left(2 x + 1\right)^{2}}\, dx = C + \sqrt{2} \left(- \frac{\sqrt{2} \left(\frac{\sqrt{2} \sqrt{x}}{2 \left(2 x + 1\right)} + \frac{\operatorname{atan}{\left(\sqrt{2} \sqrt{x} \right)}}{2}\right)}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} \right)}}{2}\right)$$
Gráfica
Respuesta
[src]
/ / ___\\
| ___ |\/ 2 ||
| \/ 2 *atan|-----||
___ |1 \ 2 /|
\/ 2 *|- + -----------------|
\6 4 /
$$\sqrt{2} \left(\frac{1}{6} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{4}\right)$$
=
=
/ / ___\\
| ___ |\/ 2 ||
| \/ 2 *atan|-----||
___ |1 \ 2 /|
\/ 2 *|- + -----------------|
\6 4 /
$$\sqrt{2} \left(\frac{1}{6} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{4}\right)$$
sqrt(2)*(1/6 + sqrt(2)*atan(sqrt(2)/2)/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.