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$\int_{0}^{\frac{3\pi}{2}}\frac{\cos\left(x\right)}{1+\sin\left(x\right)^2}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function cos(x)/(1+sin(x)^2) from 0 to (3*pi)/2. Simplifying. We can solve the integral \int\frac{\cos\left(x\right)}{1+\sin\left(x\right)^2}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get.