How do I find this integral using weierstrass substitution?
1/(9-4((sinx)^2))
To find the integral using the Weierstrass substitution, follow these steps:
1. Start by using the Weierstrass substitution: set `(sin(x))^2 = (3/2)*(1 - cos(2x/3))`. This substitution simplifies the integral by eliminating the trigonometric function.
2. Rewrite the integral with the new substitution: `∫[1/(9 - 4((sin(x))^2))] dx` becomes `∫[1/(9 - 4*(3/2)*(1 - cos(2x/3)))] dx`.
3. Simplify the expression inside the integral: `9 - 4*(3/2)*(1 - cos(2x/3)) = 9 - 6*(1 - cos(2x/3)) = 9 - 6 + 6*cos(2x/3) = 3 + 6*cos(2x/3)`.
4. Substitute the new expression into the integral: `∫[1/(3 + 6*cos(2x/3))] dx`.
5. You now have an integral in terms of `cos(2x/3)`. To evaluate this integral, use the standard techniques for integrating functions that involve trigonometric functions.
6. After finding the antiderivative, write down the integral's answer.