Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Weierstrass Substitution
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Simplifying
Learn how to solve definite integrals problems step by step online.
$\int_{0}^{\frac{3\pi}{2}}\frac{\cos\left(x\right)}{1+\sin\left(x\right)^2}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function cos(x)/(1+sin(x)^2) from 0 to 3/2pi. 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.