Sr Examen
Integral de (5*x*x+1)^(1/2) dx
Solución
Ha introducido
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2 / | | ___________ | \/ 5*x*x + 1 dx | / 1
$$\int\limits_{1}^{2} \sqrt{x 5 x + 1}\, dx$$
Integral(sqrt((5*x)*x + 1), (x, 1, 2))
Respuesta (Indefinida)
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/ __________ | / 2 ___ / ___\ | ___________ x*\/ 1 + 5*x \/ 5 *asinh\x*\/ 5 / | \/ 5*x*x + 1 dx = C + --------------- + -------------------- | 2 10 /
$$\int \sqrt{x 5 x + 1}\, dx = C + \frac{x \sqrt{5 x^{2} + 1}}{2} + \frac{\sqrt{5} \operatorname{asinh}{\left(\sqrt{5} x \right)}}{10}$$
Gráfica
Respuesta
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___ ___ / ___\ ___ / ___\
____ \/ 6 \/ 5 *asinh\\/ 5 / \/ 5 *asinh\2*\/ 5 /
\/ 21 - ----- - ------------------ + --------------------
2 10 10
$$- \frac{\sqrt{6}}{2} - \frac{\sqrt{5} \operatorname{asinh}{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \operatorname{asinh}{\left(2 \sqrt{5} \right)}}{10} + \sqrt{21}$$
=
=
___ ___ / ___\ ___ / ___\
____ \/ 6 \/ 5 *asinh\\/ 5 / \/ 5 *asinh\2*\/ 5 /
\/ 21 - ----- - ------------------ + --------------------
2 10 10
$$- \frac{\sqrt{6}}{2} - \frac{\sqrt{5} \operatorname{asinh}{\left(\sqrt{5} \right)}}{10} + \frac{\sqrt{5} \operatorname{asinh}{\left(2 \sqrt{5} \right)}}{10} + \sqrt{21}$$
sqrt(21) - sqrt(6)/2 - sqrt(5)*asinh(sqrt(5))/10 + sqrt(5)*asinh(2*sqrt(5))/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.