Mastering Antiderivatives: Solving Challenging Problems with U-Substitution

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The discussion revolves around solving the integral ∫(x² + 3x + 7)/√x dx. The user initially struggles with finding an algebraic method and considers using u-substitution to simplify the problem. After some contemplation, they realize that dividing the terms can lead to a straightforward solution. The user expresses frustration over spending time on the problem before arriving at the answer independently. Ultimately, the conversation highlights the importance of perseverance and the learning process in mastering antiderivatives.
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Homework Statement


Find \int \frac{x^{2}+3x+7}{\sqrt{x}}dx


Homework Equations





The Attempt at a Solution




I am reviewing for a test on tuesday. I can't see a good algebraic method to solve this using the fact that \int f(g(x))g'(x)dx=F(g(x))+C so I am starting to think it requires a u-substitution which I am trying to get better at right now before the test. Can someone point me in the right direction here? Thankyou very much, I appreciate any help!
 
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Duh nevermind, I can just divide out the terms... *Sigh* I always spend lots of time on a problem, post it here, and then 3 minutes later I figure it out... Grr, sorry!

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