1/5 / | | ___ -x | \/ x *e dx | / 0
Integral(sqrt(x)*exp(-x), (x, 0, 1/5))
UpperGammaRule(a=-1, e=1/2, context=sqrt(x)*exp(-x), symbol=x)
Add the constant of integration:
The answer is:
/ | ____ / ___\ | ___ -x ___ -x \/ pi *erfc\\/ x / | \/ x *e dx = C - \/ x *e - ------------------ | 2 /
/ ___\ ____ |\/ 5 | \/ pi *erf|-----| ___ -1/5 \ 5 / \/ 5 *e ----------------- - ----------- 2 5
=
/ ___\ ____ |\/ 5 | \/ pi *erf|-----| ___ -1/5 \ 5 / \/ 5 *e ----------------- - ----------- 2 5
sqrt(pi)*erf(sqrt(5)/5)/2 - sqrt(5)*exp(-1/5)/5
Use the examples entering the upper and lower limits of integration.