Hey Guys,

Can someone please explain to me why the constant isn't used in the v of the u●v part of the formula?

I.e. Integral u●dv = integral u●v - integral v●du

For example Integral x cos (x) dx

Let x = u and dv = cos(x)dx, then du = 1 and v = sin(x)+c1

=> Integral x cos (x)dx = x sin(x)+c1 - Integral sin(x)+c1 dx

= x sin(x)+c1 - (Integral sin(x)dx + Integral c1 dx)

= x sin(x)+c1 - (cos(x) + c2 + c1x +c2))

= x sin(x)+c1 + cos(x) - c2 - c1x - c2

=> x sin(x) +c1 + cos(x) - c2 - c1x - c2 = x sin(x) +c1 + cos(x) - c1x - 2c2 .

Now the generic solution is xsin(x) + cos(x) + c.

What am I doing wrong?

Thanks.