Can someone help me with some intergral work?

Question

I have a few questions on this take home quiz and I have no iea how to do it

1) intergral of: (dx)/(e^(2x)+5)

2) intergral of: (x+3)/(x^2+9)

3) intergral of: (sin2x)/(1+cos^2(2x))

I now for the third one a trig identity is involved but I don't know how to do the rest

Answer 1

1)

Do partial fractions.

Constant => 5 A = 1 => A = 1/5.

v coefficient => A + B = 0 => 1/5 + B = 0 => B = -1/5.

 

Answer 2

2)

Substitute u and v values.

Answer 3

3)

Substitute v value.

Substitute u value.