Show the work please, just having answers doesnt really help. First to answer co

Question

Show the work please, just having answers doesnt really help. First to answer correctly with good work shown will get rated.

1) int dx/sqrt(9-x^2)
2) int (11/(36+x^2)) dx
3) int (1/(4+(x-3)^2)) dx
4) int (1/(x sqrt(x^4 -4)) dx
5) int ((e^2x)/(4+e^4x)) dx
6) int (sec^2 x)/(sqrt(25-tan^2 x)) dx
7) int (1/((sqrtx)sqrt(1-x))) dx
8) int ((x-3)/(x^2 +1)) dx

9) int (3/(sqrt(1-9x^2))) dx from 0 to 1/6
10) int ((e^-x)/(sqrt(1-e^-2x))) dx from ln2 to ln4

11) int (dx/(x^2 - 2x + 2)) from 0 to 2
12) int ((2x-5)/(x^2 + 2x + 2)) dx

Explanation / Answer

1. let x/3=sint, then x=3*sint, dx=3*dt*cost, t=asin(x/3);

y(t)*dt =(1/3) *3*dt*cost / sqrt(1-(sint)^2) = dt, hence
?*y(t)*dt =?dt =t = asin(x/3) +C;

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