Integration of (e^x/(1+e^2x)) dx and integration(dy/(y^2+6y+10...?

Question

can some body help me with this

Answer 1

1. ∫ (e^x / (1 + e^2x)) dx
Let u = e^x, then du = e^x dx
∫ (e^x dx / (1 + e^2x))
= ∫ (du / (1 + u^2))
= arctan u + c
= arctan e^x + c.

2. ∫(dy / (y^2 + 6y + 10))
Let u = y + 3, then du = dy and u^2 = y^2 + 6y + 9
∫(dy / (y^2 + 6y + 10))
= ∫(du / (u^2 + 1))
= arctan u + c
= arctan (y+3) + c.

Answer 2

oh yeah thats simple the answer is
EGG