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

[KungPeng Zhou]

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.

 

[anuttarasammyak]

Try putting ##[tex]$at head and$[/tex]## at tail of your math code to show it properly.

 

[KungPeng Zhou]

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.

 

[PeroK]

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.

If you reply to a thread with Latex, you can copy and paste the Latex to your post. Then abandon the reply. Try this post from your other thread:

https://www.physicsforums.com/threa...f-upper-bound-integrals.1055220/#post-6926653

 

[pasmith]

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 [itex]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
But the question，it seems that I can't use the way to solve the question.I can't find a correct commutation method.

Did you consider $t = x + 2$, $dx = dt$?

 

[anuttarasammyak]

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.

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

Why don't you try these two ways for Latex in your post ?

 

[fresh_42]

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/.

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

 

[KungPeng Zhou]

Did you consider $t = x + 2$, $dx = dt$?

Ithe seems that we still can't solve it with this way...

 

[pasmith]

Ithe seems that we still can't solve it with this way...

You can't integrate $\int (t - 2)^2\sqrt{t}\,dt = \int t^{5/2} - 4t^{3/2} + 4t^{1/2}\,dt$?

 

[KungPeng Zhou]

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.