Some integrals with problematic evaluation

[quinyu]

In that integral, that is exactly what is done. For an integral of the shape Int((cos(c+dx)^2*b+a)^p,x), you can rewrite with tan(c+dx)/e, where e is the product of the factors in tan(c+dx) free of x. Then the integral takes the shape Int(1/(5+2u^2),u). An integral of the shape Int(1/(a+bx^2),x) results in sqrt(a/b)atan(x/sqrt(a/b))/a. Putting it all together, we get x/sqrt(10) - atan(3sin(x)cos(x)/(2+sqrt(10)+3cos(x)^2))/sqrt(10).

Is it useful this way, Mr. Parisse? (And I truly would like to know if there is a way to input, say, TeX code here for a nicer display... if I start typing formulas like this, it's bound to be rather difficult to read.)