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

[4unitmath]

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]

 

[bobmcbob365]

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]

;~; 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.

 

[bobmcbob365]

<3 Happy to help.

 

[4unitmath]

but how would you integrate x^2.tan^-1(x)..?

 

[4unitmath]

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

 

[bobmcbob365]

^^