13:: Is it not an hypergeometric Function ! Substituting x=2sina gives u
5 Answers
62First one: (x2+1)3+4(x4+x2)x3−x=(x+1/x)3+4(x+1/x)1−1/x2
623) the standard trick that we often use to convert this to cos 3 theta
x=kt
3x-x3=3kt - k3t3=k(3t - k2t3)
so for the substitution of sin theta, we want k2=4
so we substitute k=2
so we will end up with x=2t
Substitute t= sin theta, thsi will get converted to sin 3 theta
here this method will not give as good benefits as i initally thought.. but now that i have typed so much the idea can be tehre on how to convert a cubic to cos 3x form :P
1
262for 2nd problem, just multiply numberator and denominator with x.
bring x inside the root in the denominator.
then take the part inside the denominator as t.
then dt will be a constant mutiple of the numerator.
∫√[2012]2012.x2013+2013.x2012x2012+x2011dx
now 2012.x2013+2013.x2012=t
2012.2013.(x2011+x2012)dx=dt
nothing more to say after that.
