Hi, Sorry but, would someone of you so kindly help me with a particular integral that I have problems with?

I would deeply appreciate it.

Now here it goes.



Trigonometrical substitution.
S='integral of.'

S(4+x^2)^.5dx

that means, integral of the square root of 4 plus x squared

This particular case is of the form of S(a^2+x^2)^.5

thus we use

x=atan( t)

x=2tan(t )
dx= 2sec^2(t )dt

Thus

S((4+4tan^2(t ))^.5)*2sec^2 (t )dt

moving some numbers... (1+tan^2 (t )=sec^2( t))
4 S ((sec^2( t))^.5)*sec^2( t)
then I simplified to

4*( S sec^3( t)dt)

then I got stuck.

Help please? Am I doing something wrong?