As you know, they are both right angled triangles.
For 45 degree ratios use a right angles isosceles triangle where the 2 equal sides are both 1 unit.
Find the hypotenuse using pythagoras's theorem and then read off the ratio values from it.
For both 60degrees and 30degrees.
Start with a equilateral triangle with side length 2 units.
Then cut it in half to get two congruent triangles, you will only use one of them.
it has a right angle, a 30degree angle and a 60 degree angle,
the hypotenuse is 2 units and one side is 1 unit.
Use pyth to find the 3rd side and that is it.
1. 2 0[1/((sqrt1+x^3)) dx
This is what you asked for, I suspect it is not what you really want. Be careful with your brackets.
Is this what you want?
Integral from 0 to 2 of [1/(sqrt[1+x^3]) dx