Sr Examen
Integral de 3^sqrt(6x-2) dx
Solución
Ha introducido
[src]
3 / | | _________ | \/ 6*x - 2 | 3 dx | / 0
$$\int\limits_{0}^{3} 3^{\sqrt{6 x - 2}}\, dx$$
Integral(3^(sqrt(6*x - 2)), (x, 0, 3))
Respuesta (Indefinida)
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/ | ___ __________ ___ __________ | _________ \/ 2 *\/ -1 + 3*x ___ \/ 2 *\/ -1 + 3*x __________ | \/ 6*x - 2 3 \/ 2 *3 *\/ -1 + 3*x | 3 dx = C - ------------------- + -------------------------------------- | 2 3*log(3) / 3*log (3)
$$\int 3^{\sqrt{6 x - 2}}\, dx = \frac{\sqrt{2} \cdot 3^{\sqrt{2} \sqrt{3 x - 1}} \sqrt{3 x - 1}}{3 \log{\left(3 \right)}} - \frac{3^{\sqrt{2} \sqrt{3 x - 1}}}{3 \log{\left(3 \right)}^{2}} + C$$
Gráfica
Respuesta
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___ ___
I*\/ 2 ___ I*\/ 2
27 108 3 I*\/ 2 *3
- ------- + ------ + --------- - ----------------
2 log(3) 2 3*log(3)
log (3) 3*log (3)
$$- \frac{27}{\log{\left(3 \right)}^{2}} + \frac{108}{\log{\left(3 \right)}} - \frac{\sqrt{2} \cdot 3^{\sqrt{2} i} i}{3 \log{\left(3 \right)}} + \frac{3^{\sqrt{2} i}}{3 \log{\left(3 \right)}^{2}}$$
=
=
___ ___
I*\/ 2 ___ I*\/ 2
27 108 3 I*\/ 2 *3
- ------- + ------ + --------- - ----------------
2 log(3) 2 3*log(3)
log (3) 3*log (3)
$$- \frac{27}{\log{\left(3 \right)}^{2}} + \frac{108}{\log{\left(3 \right)}} - \frac{\sqrt{2} \cdot 3^{\sqrt{2} i} i}{3 \log{\left(3 \right)}} + \frac{3^{\sqrt{2} i}}{3 \log{\left(3 \right)}^{2}}$$
-27/log(3)^2 + 108/log(3) + 3^(i*sqrt(2))/(3*log(3)^2) - i*sqrt(2)*3^(i*sqrt(2))/(3*log(3))
Respuesta numérica
[src]
(76.3688331271892 + 0.269352691188596j)
(76.3688331271892 + 0.269352691188596j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.