- ∫ sqrt(x^2-2/9-35/81 +(1/81))

*Complete the square*

- ∫ sqrt (x+(1/9)^2)

So, (x + (1/9)) = 2/3 tan θ

(3/2)x + 1/6= tan θ

I then used u-substitution, where u = 2/3 tan θ and du= 2/3 sec^2θ dθ

-∫ 36dθ/ u^2+(4/9)

-36 ∫ (2/3) sec^2θ/ (2/3) secθ

= -36∫ secθ

=-36 | secθtanθ| + C

θ= arctan (3/2)x+(1/6)

I have typed this into my Webwork, and yet the solution is wrong...any suggestions are welcome.

Also,

I am unsure where to start for this problem:

∫e^(7x)/(e^(14x)+36)dx

Would I use the natural log?

Thanks so much in advance!

-Nikayla