## anonymous 5 years ago alriiight, not sure on how to answer this: Evaluate the integral: ∫[(e^(4√(z)))/(√(z)),z] image of question: http://www.mathway.com/math_image.aspx?p=SMB02ASMB03integral,SMB02FSMB03eSMB02ESMB034SMB02RSMB03zSMB02rSMB03SMB02eSMB03SMB10SMB02RSMB03zSMB02rSMB03SMB02fSMB03,zSMB02aSMB03?p=71?p=44

1. anonymous

do substitution: u=sq root (z) so, du=1/2 * 1/sq.rt (z) it's become easy integral (2*e^4u)du finish it

2. anonymous

You can treat the denominator as z^-1/2 and use the product rule $[f \prime (x) g(x) + g \prime(x) f(x)]$ or just use the quotient rule. The derivative of e^u is $u \prime e ^{u}$

3. anonymous

2*integral(e^4u)du = 2* 1/4 *e^4u = 1/2* e^sw.rt(z)