Need a little help; have to use itegration by parts. Thanks

[jbevins1]

integral of exp(sqrt(x))

 

[Guest]

int e^sqrt(x) dx

= int sqrt(x) * e^sqrt(x) / sqrt(x) dx

= int (sqrt(x) * e^sqrt(x) / sqrt(x) + 1 / (2 * sqrt(x)) * 2 * e^sqrt(x) - 1 / (2 * sqrt(x)) * 2 * e^sqrt(x)) dx

= int (sqrt(x) * d/dx (2 * e^sqrt(x)) + (d/dx sqrt(x)) * 2 e^sqrt(x)) dx - int 1 / (2 * sqrt(x)) * 2 * e^sqrt(x) dx

= sqrt(x) * 2 * e^sqrt(x) - int e^sqrt(x) / sqrt(x) dx

= sqrt(x) * 2 * e^sqrt(x) - 2 int e^sqrt(x) / (2 * sqrt(x)) dx

= sqrt(x) * 2 * e^sqrt(x) - 2 int (d/dx e^sqrt(x)) dx

= 2 * sqrt(x) * e^sqrt(x) - 2 * e^sqrt(x) + C

 

[Matt]

Hi jbevins1,

One way to solve this problem is to take

. . . . u = e^√x, and
. . . . dv = dx

so that du=[e^√x/(2√x)]dx and v=x, and:

. . . .

Then on this last integral, perform the substitution

. . . . u = √x,
. . . . du = dx/(2√x)

to obtain:

. . . .

Can you finish the integration on your own?

 

[jbevins1]

Thanks for all of the help; that really helped me out.