Integrating Calc Equations: U-Substitution Solutions

[Entropy]

Okay, I just failed my Calc quiz and I want to know how to do the problems I missed. I failed to integrate two of the three equations that were given. The two I missed were:

$$\int\sqrt{1 + e^x}dx$$

$$\int\frac{\arctan{\sqrt{t}}}{\sqrt{t}}dt$$

Nothing like this is in our book, I don't know where she gets these problems from. She said we're suppose to use some type of u-substitution but I can't figure out which. Can someone walk me through this?

 

[TD]

Try the following substitutions:

$$t = \sqrt{1+e^x}$$

$$u = \sqrt{t}$$

 

[amcavoy]

Try the following substitutions:

$$t = \sqrt{1+e^x}$$

$$u = \sqrt{t}$$

You may need to use integration by parts as well.