Sr Examen
Integral de 2arctgsqrt(x/(1+x)) dx
Solución
Ha introducido
[src]
1 / | | / _______\ | | / x | | 2*atan| / ----- | dx | \\/ 1 + x / | / 0
$$\int\limits_{0}^{1} 2 \operatorname{atan}{\left(\sqrt{\frac{x}{x + 1}} \right)}\, dx$$
Integral(2*atan(sqrt(x/(1 + x))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /
| | |
/ / _______\ | _______ / _______\ | _______ | _______
| | / x | | / x | / x | | / x | 2 / x
| / _______\ log|-1 + / ----- | | x* / ----- log|1 + / ----- | / _______\ | x* / ----- | x * / ----- / _______\
| | / x | \ \/ 1 + x / | \/ 1 + x \ \/ 1 + x / | / x | | \/ 1 + x | \/ 1 + x | / x |
| 2*atan| / ----- | dx = C + --------------------- - | ------------- dx - -------------------- + 2*x*atan| / ----- | + | -------------- dx + | -------------- dx + atan| / ----- |
| \\/ 1 + x / 2 | 1 + 2*x 2 \\/ 1 + x / | 2 | 2 \\/ 1 + x /
| | | 1 + 2*x + 3*x | 1 + 2*x + 3*x
/ / | |
/ /
$$\int 2 \operatorname{atan}{\left(\sqrt{\frac{x}{x + 1}} \right)}\, dx = C + 2 x \operatorname{atan}{\left(\sqrt{\frac{x}{x + 1}} \right)} + \frac{\log{\left(\sqrt{\frac{x}{x + 1}} - 1 \right)}}{2} - \frac{\log{\left(\sqrt{\frac{x}{x + 1}} + 1 \right)}}{2} + \operatorname{atan}{\left(\sqrt{\frac{x}{x + 1}} \right)} - \int \frac{x \sqrt{\frac{x}{x + 1}}}{2 x + 1}\, dx + \int \frac{x \sqrt{\frac{x}{x + 1}}}{2 x^{2} + 3 x + 1}\, dx + \int \frac{x^{2} \sqrt{\frac{x}{x + 1}}}{2 x^{2} + 3 x + 1}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.