$\displaystyle \int( \sqrt[3]{u} + \cos2u + e^{-u} )du$
e = Exponential
Some reminders:
$\displaystyle \int \sqrt[3]{u}~du = \int u^{1/3}~du$
Use the power rule for integration.
$\displaystyle \int cos(2u)~du$
Use the substitution x = 2u. Then you need to know
$\displaystyle \int cos(x)~dx = sin(x) + C$.
(This is not the answer. There's a multiplicative factor too.)
$\displaystyle \int e^u~du = e^u + C$
Let x = -u. Then you need to know
$\displaystyle \int e^x~dx = e^x + C$
-Dan
How could that possibly be the answer? You are adding the terms in the integrand, so you wouldn't multiply. And I presume that your question is asking you to integrate, so do the integrals.
Or is the question actually to integrate
$\displaystyle \int u^{1/3}~sin(2u)~e^u~du$
-Dan