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mickellowery
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What method would I use to integrate cos(x)/1+sin^2(x)dx? I was thinking by parts but it isn't working for me.
Try a u substitution.mickellowery said:What method would I use to integrate cos(x)/1+sin^2(x)dx? I was thinking by parts but it isn't working for me.
mickellowery said:What method would I use to integrate cos(x)/1+sin^2(x)dx? I was thinking by parts but it isn't working for me.
The integration method for cos(x)/1+sin^2(x)dx is to use the substitution method. Let u = sin(x) and du = cos(x)dx, then the integral becomes ∫du/(1+u^2), which can be solved using partial fractions or by using the inverse tangent function.
Yes, the integral cos(x)/1+sin^2(x)dx can also be solved using trigonometric identities, specifically tan^2(x) + 1 = sec^2(x). This will result in an integral of the form ∫sec^2(x)/(1+tan^2(x)), which can be solved using the substitution method mentioned above.
Yes, apart from the substitution and trigonometric identities method, this integral can also be solved using the Weierstrass substitution. Let u = tan(x/2), then the integral becomes ∫2du/(u^2+1). This can be solved using partial fractions or by using the inverse hyperbolic tangent function.
No, there is no shortcut or trick to solving this integral. It requires knowledge of various integration techniques and the ability to recognize the appropriate method to use in each case.
Yes, this integral can be solved using various software or online calculators that have the ability to perform symbolic integration. However, it is important to have a basic understanding of the integration methods involved in order to verify the accuracy of the result.