Sr Examen
Integral de sqrt(7x+2)*e^(-3x) dx
Solución
Ha introducido
[src]
oo / | | _________ -3*x | \/ 7*x + 2 *E dx | / 2
$$\int\limits_{2}^{\infty} e^{- 3 x} \sqrt{7 x + 2}\, dx$$
Integral(sqrt(7*x + 2)*E^(-3*x), (x, 2, oo))
Respuesta (Indefinida)
[src]
/ / ____ _________\ \
| ____ |\/ 21 *\/ 2 + 7*x | |
|\/ pi *erfc|------------------| ____ _________ -6/7 - 3*x|
/ ____ | \ 7 / \/ 21 *\/ 2 + 7*x *e | 6/7
| \/ 21 *|------------------------------- + ------------------------------|*e
| _________ -3*x \ 2 7 /
| \/ 7*x + 2 *E dx = C - ------------------------------------------------------------------------------
| 9
/
$$\int e^{- 3 x} \sqrt{7 x + 2}\, dx = C - \frac{\sqrt{21} \left(\frac{\sqrt{21} \sqrt{7 x + 2} e^{- 3 x - \frac{6}{7}}}{7} + \frac{\sqrt{\pi} \operatorname{erfc}{\left(\frac{\sqrt{21} \sqrt{7 x + 2}}{7} \right)}}{2}\right) e^{\frac{6}{7}}}{9}$$
Respuesta
[src]
/ / / ____\ \ \
| | |4*\/ 21 | | |
| |89*erf|--------| ____ -48/7| |
| ____ ____ | \ 7 / 2*\/ 21 *e | / ____\|
| \/ 21 *\/ pi *|---------------- + ---------------| ____ ____ |4*\/ 21 ||
| | 12 ____ | 8*\/ 21 *\/ pi *erf|--------||
| \ 3*\/ pi / \ 7 /| 6/7
2*|- -------------------------------------------------- + -----------------------------|*e ____ ____ 6/7
\ 3 3 / \/ 21 *\/ pi *e
- --------------------------------------------------------------------------------------------- + ------------------
7 18
$$- \frac{2 \left(- \frac{\sqrt{21} \sqrt{\pi} \left(\frac{2 \sqrt{21}}{3 \sqrt{\pi} e^{\frac{48}{7}}} + \frac{89 \operatorname{erf}{\left(\frac{4 \sqrt{21}}{7} \right)}}{12}\right)}{3} + \frac{8 \sqrt{21} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{21}}{7} \right)}}{3}\right) e^{\frac{6}{7}}}{7} + \frac{\sqrt{21} \sqrt{\pi} e^{\frac{6}{7}}}{18}$$
=
=
/ / / ____\ \ \
| | |4*\/ 21 | | |
| |89*erf|--------| ____ -48/7| |
| ____ ____ | \ 7 / 2*\/ 21 *e | / ____\|
| \/ 21 *\/ pi *|---------------- + ---------------| ____ ____ |4*\/ 21 ||
| | 12 ____ | 8*\/ 21 *\/ pi *erf|--------||
| \ 3*\/ pi / \ 7 /| 6/7
2*|- -------------------------------------------------- + -----------------------------|*e ____ ____ 6/7
\ 3 3 / \/ 21 *\/ pi *e
- --------------------------------------------------------------------------------------------- + ------------------
7 18
$$- \frac{2 \left(- \frac{\sqrt{21} \sqrt{\pi} \left(\frac{2 \sqrt{21}}{3 \sqrt{\pi} e^{\frac{48}{7}}} + \frac{89 \operatorname{erf}{\left(\frac{4 \sqrt{21}}{7} \right)}}{12}\right)}{3} + \frac{8 \sqrt{21} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{21}}{7} \right)}}{3}\right) e^{\frac{6}{7}}}{7} + \frac{\sqrt{21} \sqrt{\pi} e^{\frac{6}{7}}}{18}$$
-2*(-sqrt(21)*sqrt(pi)*(89*erf(4*sqrt(21)/7)/12 + 2*sqrt(21)*exp(-48/7)/(3*sqrt(pi)))/3 + 8*sqrt(21)*sqrt(pi)*erf(4*sqrt(21)/7)/3)*exp(6/7)/7 + sqrt(21)*sqrt(pi)*exp(6/7)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.