Can't Find a Correct Method to Integrate \int (t - 2)^2\sqrt{t}\,dt?

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Homework Statement
\int x^{2}\sqrt{2+x}dx
Relevant Equations
The Substitution Rule,
Table of Indefinite Integrals
When I encountereD this kind of question before.For example
\int x\sqrt{2+x^{2}}dx
We make the Substitution t=x^{2}+2,because its differential is dt=2xdx,so we get \int x\sqrt{2+x^{2}}=1/2\int\sqrt{t}dt,then we can get the answer easily
But the question,it seems that I can't use the way to solve the question.I can't find a correct commutation method.
 
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Try putting #### at head and #### at tail of your math code to show it properly.
 
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Sorry,but I can't understand you.Could you please tell how to show my math code properly?Now I just can use these math code.
 
KungPeng Zhou said:
Homework Statement: \int x^{2}\sqrt{2+x}\,dx
Relevant Equations: The Substitution Rule,
Table of Indefinite Integrals

When I encountereD this kind of question before.For example
\int x\sqrt{2+x^{2}}\,dx
We make the Substitution t=x^{2}+2,because its differential is dt=2xdx[/tex],so we get \int x\sqrt{2+x^{2}}\,dx =\frac12 \int\sqrt{t}\,dt, then we can get the answer easily<br /> But the question,it seems that I can&#039;t use the way to solve the question.I can&#039;t find a correct commutation method.<br />
<br /> <br /> Did you consider t = x + 2, dx = dt?
 
KungPeng Zhou said:
Sorry,but I can't understand you.Could you please tell how to show my math code properly?Now I just can use these math code.
1693222343057.png


Example for \frac{\pi}{2}
##\frac{\pi}{2}##
\frac{\pi}{2}

Why don't you try these two ways for Latex in your post ?
 
KungPeng Zhou said:
Sorry,but I can't understand you.Could you please tell how to show my math code properly?Now I just can use these math code.
Look at https://www.physicsforums.com/help/latexhelp/.
KungPeng Zhou said:
Homework Statement: ##\int x^{2}\sqrt{2+x}dx##
Relevant Equations: The Substitution Rule,
Table of Indefinite Integrals

When I encountereD this kind of question before.For example
##\int x\sqrt{2+x^{2}}dx##
We make the Substitution ##t=x^{2}+2##,because its differential is ##dt=2xdx##,so we get ##\int x\sqrt{2+x^{2}}=1/2\int\sqrt{t}dt##,then we can get the answer easily
But the question,it seems that I can't use the way to solve the question.I can't find a correct commutation method.
I'm not quite sure what you actually want to know. The LaTeX issue is addressed above and in the link.

The integral works as follows and is explained here:
https://www.physicsforums.com/threads/substitution-in-a-definite-integral.1054611/#post-6919864
 
pasmith said:
Did you consider t = x + 2, dx = dt?
Ithe seems that we still can't solve it with this way...
 
KungPeng Zhou said:
Ithe seems that we still can't solve it with this way...

You can't integrate \int (t - 2)^2\sqrt{t}\,dt = \int t^{5/2} - 4t^{3/2} + 4t^{1/2}\,dt?
 
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pasmith said:
You can't integrate \int (t - 2)^2\sqrt{t}\,dt = \int t^{5/2} - 4t^{3/2} + 4t^{1/2}\,dt?
Yes,you are right.
 
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