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Integration by substitution
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You are currently reading a thread in /sci/ - Science & Math

File: Calc2_WK1_Prompt2.png (40 KB, 657x148) Image search: [iqdb] [SauceNao] [Google]
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Hi /sci/. My prof presented this problem as part of our first week of homework. He wants us to solve it with substitution and integration by parts, but I don't think we can progress with substitution. Even if we take his suggestion for u to start with, it just derives into 1dx, which now leaves us with two dx's, one of which is under a root. Am I wrong, or does substitution just not work here?
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>>7775960
Do integration by parts first and see what happens.
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>>7775960
I don't think you understand substitution...
if u = x+1, you need to express du as a function of dx.
Here it's easy: du = dx
then you need to substitute the function of x in the integral with a new (and equivalent) function of u.

x^2sqrt(x+1)dx = (u-1)^2 sqrt(u) du
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>>7775960youI would substitute yourself for him when it comes fucking his wife and daughter
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>>7775967
And how do you integrate the new function?
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>>7775967
Hadn't thought of replacing the x^2 with(u-1)^2. That's definitely a tool I'm going to remember for later... But you still can't integrate the new function, can you? Maybe with another round of replacement....
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>>7775975
yee budy id bngag them so hard
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>>7775987
[eqn] (u-1)^2 \sqrt{u} = u^{ 5/2 } -2 u^{ 3/2 } + \sqrt{u{ [/eqn]
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>>7775960
"seemingly different answers" ? After you put x back in after substitution and integration? I'm skeptical.
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>>7775967
>if u = x+1, you need to express du as a function of dx.
ewwww fucking normies
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>>7775991
you need to substitute s=sqrt(u) and everything will work out.

don't forget to add boundaries and to modify them accordingly if you make a change of variables.
if x goes from 0 to t, u will go from 1 to t+1, and s will go from 1 to sqrt(t+1)
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>>7776091
fuck off asshat.
He's trying to learn, each step counts.
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>>7776100
no, you're just a retard breeding other retards
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File: 1434208727862.gif (924 KB, 180x172) Image search: [iqdb] [SauceNao] [Google]
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>Americans don't even know how to integrate rational functions with goniometric and / or square root funictions

TOP 10 MY FUCKING ASS HAHAHAHAHA

>Calculus

Not even once, my friends. ;)
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>>7776093
>Triple substitution with a simple integration problem

>>7776132