How many positive integer solutions (a,b,c) to 2a+3b+3c=2010

Solve the equation y"-4y=lnx ?

Find the value of the integral I=∫√(tanx)dx

Find the value of the integral I=∫√(sinx)dx

Let r is radius of circle inscribed and R is radius of circle circumscribing atriangle ABC.

Prove that p[tan(A/2)+tan(A/2)+tan(A/2)]=r+4R where p=(1/2)(a+b+c).