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Mathematics: Post your doubts here!

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Can anyone explain to me how to solve these questions? Thank You.

Intergrate the following functions with respect to x.
1. x^2 cos x
2. In (x-1)
3. (In x)^2
 
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Hey!! Can someone please help me with M/J 2012 P33 Q10. Been stuck here for so long :( thanks!

Hey, I have just solved this for you it's attached here :) hopefully I'm correct
 

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Can someone help me with this question! After getting the equation, I don't know how to rearrange it to get the final answer :confused:
 

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upload_2015-4-29_12-13-21.png

How do you do part (iii) ?
I always get confused on how to do it when it's a bracket within a bracket... please help!
 
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Have you tried using

(1+x)^n = 1 + nx + (n(n-1)/2!) x^2 +........... ?

It says hence find the co-eff
By doing the expansion
5C4 x 1 x (x + 3x^2)^4
I get the co-eff to be 405

Then in part ii, the co-eff is 270
And in part i, the co-eff is 81

What they have done is added 405 and 270 to give co-eff = 675
But then why not add 81 to it ... and why add 270 to it ? :confused::(
 
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It says hence find the co-eff
By doing the expansion
5C4 x 1 x (x + 3x^2)^4
I get the co-eff to be 405

Then in part ii, the co-eff is 270
And in part i, the co-eff is 81

What they have done is added 405 and 270 to give co-eff = 675
But then why not add 81 to it ... and why add 270 to it ? :confused::(
How did you expand (x+3x^2)^4?
 
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View attachment 52686

How do you do part (iii) ?
I always get confused on how to do it when it's a bracket within a bracket... please help!
From your above results you can see that x^8 is when (x+3x^2)^4 and (x+3x^2)^5
Similarly in (1+(x+3x^2))^5 x^8 would be at when the expression has power of 4 and 5
So 5C4 (1) x (x+3x)^4 + 5C5 (x+3x^2)^5
Therefore 450x^8 + 270x^8 = 675x^8

Hope you understand :)
 
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