Sr Examen
Integral de arctg(x)/x^(1/2) dx
Solución
Ha introducido
[src]
2 / | | atan(x) | ------- dx | ___ | \/ x | / 0
$$\int\limits_{0}^{2} \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\, dx$$
Integral(atan(x)/sqrt(x), (x, 0, 2))
Respuesta (Indefinida)
[src]
/ | ___ / ___ ___\ ___ / ___ ___\ | atan(x) \/ 2 *log\1 + x + \/ 2 *\/ x / ___ / ___ ___\ ___ / ___ ___\ ___ \/ 2 *log\1 + x - \/ 2 *\/ x / | ------- dx = C + ------------------------------ - \/ 2 *atan\1 + \/ 2 *\/ x / - \/ 2 *atan\-1 + \/ 2 *\/ x / + 2*\/ x *atan(x) - ------------------------------ | ___ 2 2 | \/ x | /
$$\int \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\, dx = C + 2 \sqrt{x} \operatorname{atan}{\left(x \right)} - \frac{\sqrt{2} \log{\left(- \sqrt{2} \sqrt{x} + x + 1 \right)}}{2} + \frac{\sqrt{2} \log{\left(\sqrt{2} \sqrt{x} + x + 1 \right)}}{2} - \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)} - \sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}$$
Gráfica
Respuesta
[src]
___ ___ ___
___ pi*\/ 2 \/ 2 *log(20) ___ \/ 2 *log(4)
\/ 2 *atan(2) + -------- + ------------- - 2*\/ 2 *atan(3) - ------------
2 2 2
$$- 2 \sqrt{2} \operatorname{atan}{\left(3 \right)} - \frac{\sqrt{2} \log{\left(4 \right)}}{2} + \sqrt{2} \operatorname{atan}{\left(2 \right)} + \frac{\sqrt{2} \log{\left(20 \right)}}{2} + \frac{\sqrt{2} \pi}{2}$$
=
=
___ ___ ___
___ pi*\/ 2 \/ 2 *log(20) ___ \/ 2 *log(4)
\/ 2 *atan(2) + -------- + ------------- - 2*\/ 2 *atan(3) - ------------
2 2 2
$$- 2 \sqrt{2} \operatorname{atan}{\left(3 \right)} - \frac{\sqrt{2} \log{\left(4 \right)}}{2} + \sqrt{2} \operatorname{atan}{\left(2 \right)} + \frac{\sqrt{2} \log{\left(20 \right)}}{2} + \frac{\sqrt{2} \pi}{2}$$
sqrt(2)*atan(2) + pi*sqrt(2)/2 + sqrt(2)*log(20)/2 - 2*sqrt(2)*atan(3) - sqrt(2)*log(4)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.