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Integration by substitution C4

How would you integrate x(2x+1)^0.5 using 2x+1 as the substitution (u)?
I have tried making dx= du/2 and then integrating by writing everything in terms of u but can't get the right answer for some reason...

@RDKGames
(edited 7 years ago)
Original post by Uni12345678
How would you integrate x(2x+1)^0.5 using 2x+1 as the substitution (u)?
I have tried making dx= du/2 and then integrating by writing everything in terms of u but can't get the right answer for some reason...


After making the substitution and simplifying you should get:

14∫u32−u12du\frac{1}{4} \int u^\frac{3}{2} - u^\frac{1}{2} du

It might be worth posting your working.
(edited 7 years ago)
Original post by SherlockHolmes
After making the substitution and simplifying you should get:

14∫u32−u12du\frac{1}{4} \int u^\frac{3}{2} - u^\frac{1}{2} du

It might be worth posting your working.

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Sorry went through twice
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Original post by Uni12345678
...


You need to show the working to get to the integral I posted in my first post and not start from there.
Original post by SherlockHolmes
You need to show the working to get to the integral I posted in my first post and not start from there.


But I understand it already, am I doing anything wrong after that??
Original post by Uni12345678
But I understand it already, am I doing anything wrong after that??


Oh ok. The rest of your working is fine. Although, you are missing a constant of integration.
Original post by Uni12345678
But I understand it already, am I doing anything wrong after that??


Forgot the constant of integration.
Hahha thank you, but the answers given as 1/15(2x+ 1)^1.5 (3x𝑥 − 1)... +c ofc
Original post by Uni12345678
Hahha thank you, but the answers given as 1/15(2x+ 1)^1.5 (3x𝑥 − 1)... +c ofc


Yeah just get it in a different form. Start by factoring out 115u3/2\frac{1}{15}u^{3/2} and simplify what's inside the bracket.
Original post by RDKGames
Yeah just get it in a different form. Start by factoring out 115u3/2\frac{1}{15}u^{3/2} and simplify what's inside the bracket.


Thank youu

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