Sr Examen
Integral de sqrtx/(1+x^2) dx
Solución
Ha introducido
[src]
4 / | | ___ | \/ x | ------ dx | 2 | 1 + x | / 0
$$\int\limits_{0}^{4} \frac{\sqrt{x}}{x^{2} + 1}\, dx$$
Integral(sqrt(x)/(1 + x^2), (x, 0, 4))
Respuesta (Indefinida)
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/ | | ___ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ ___ / ___ ___\ | \/ 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 | 1 + x | /
$$\int \frac{\sqrt{x}}{x^{2} + 1}\, dx = C + \frac{\sqrt{2} \log{\left(- \sqrt{2} \sqrt{x} + x + 1 \right)}}{4} - \frac{\sqrt{2} \log{\left(\sqrt{2} \sqrt{x} + x + 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} - 1 \right)}}{2} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} \sqrt{x} + 1 \right)}}{2}$$
Gráfica
Respuesta
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___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
\/ 2 *atan\1 + 2*\/ 2 / \/ 2 *atan\1 - 2*\/ 2 / \/ 2 *log\20 + 8*\/ 2 / \/ 2 *log\20 - 8*\/ 2 /
----------------------- - ----------------------- - ----------------------- + -----------------------
2 2 4 4
$$- \frac{\sqrt{2} \log{\left(8 \sqrt{2} + 20 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - 2 \sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(20 - 8 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + 2 \sqrt{2} \right)}}{2}$$
=
=
___ / ___\ ___ / ___\ ___ / ___\ ___ / ___\
\/ 2 *atan\1 + 2*\/ 2 / \/ 2 *atan\1 - 2*\/ 2 / \/ 2 *log\20 + 8*\/ 2 / \/ 2 *log\20 - 8*\/ 2 /
----------------------- - ----------------------- - ----------------------- + -----------------------
2 2 4 4
$$- \frac{\sqrt{2} \log{\left(8 \sqrt{2} + 20 \right)}}{4} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - 2 \sqrt{2} \right)}}{2} + \frac{\sqrt{2} \log{\left(20 - 8 \sqrt{2} \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(1 + 2 \sqrt{2} \right)}}{2}$$
sqrt(2)*atan(1 + 2*sqrt(2))/2 - sqrt(2)*atan(1 - 2*sqrt(2))/2 - sqrt(2)*log(20 + 8*sqrt(2))/4 + sqrt(2)*log(20 - 8*sqrt(2))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.