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Evaluate {eq}\displaystyle \int \dfrac {\cos^2 (\arctan x)}{1 + x^3}\ dx {/eq}.

Question:

Evaluate {eq}\displaystyle \int \dfrac {\cos^2 (\arctan x)}{1 + x^3}\ dx {/eq}.

Integral:

The integral of the function {eq}\dfrac 1{1+x^2} {/eq} is given as {eq}\displaystyle \int \dfrac 1{1+x^2} \text dx=\tan^ {-1} x+C {/eq}. The formula to integrate the function : {eq}\cos^2(x) {/eq} is set up as {eq}\displaystyle \int \cos^2(x) \text dx=\dfrac x2+\dfrac {\sin 2(x)}{4}+C {/eq}.

Answer and Explanation: 1

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To evaluate {eq}I=\displaystyle \int \dfrac {\cos^2 (\arctan x)}{1 + x^2}\text dx {/eq}.

Let {eq}arc(\tan x)=t\implies \dfrac 1{1+x^2}=\dfrac...

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Indefinite Integrals as Anti Derivatives

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Chapter 12 / Lesson 11
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Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


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