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Intergration as a result of differentiation help please. (1 Viewer)

4unitmath

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Sorry i don't know how to use latex but..
Firstly prove that
d/dx(x^2.tan^-1(x))=2x.tan^-1(x)+1-(1)/(1+x^2)
That part was pretty simple but
b)Hence prove that Integral from 0 to root 3, xtan^-1(x)dx= 2pi/3 -root3/2
Thanks in advance.
 

bobmcbob365

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So basically in these types of questions, you split up the integral. Keep the part that you proved in part (a) (i.e. xtan^-1(x)) on one side, and chuck everything else on the other side.
Then integrate like you normally would.
 

4unitmath

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;~; bobmcbob365, you will forever be ingrave in my heart. too bad you can't rep any more TT__TT but thank you for your help.
 

4unitmath

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oh wait lol you don't need to haha never mind bobmcbobby ^^__^^^^
 

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