SOLUTION: hy i have this math problem and its really stressing me out can anyone help?..i have to find the integration by parts of e^-sqrt of X

Question 1079635: hy i have this math problem and its really stressing me out can anyone help?..i have to find the integration by parts of e^-sqrt of X

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
integrate e^-sqrt(x)
:
let u = sqrt(x) and du = (1/(2*sqrt(x)))dx
:
integral e^-sqrt(x) = 2 * integral (e^-u) * u * du
:
integrate by parts
:
f = u, dg = e^-u * du
df = du, g = -e^-u
:
= (-2e^-u)u + 2 * integral (e^-u)du
:
for the integral e^-u substitute s = -u and ds = -du
:
= -(2e^-u) * u + 2 * integral (e^s) * ds + constant
:
the integral of e^s is e^s
;
= -2e^s - (2e^-u) * u + constant
:
substitute s = -u
:
= (-2e^-u)u - (2e^-u) + constant
:
substitute u = sqrt(x)
:
= (-2e^-sqrt(x))*sqrt(x) - (2e-sqrt(x)) + constant
:
******************************************
= -2e^-sqrt(x) * (sqrt(x) + 1) + constant
******************************************
:

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