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Evaluate using integration by parts:

{eq}\displaystyle \int \tan^{-1} x\ dx {/eq}.

Question:

Evaluate using integration by parts:

{eq}\displaystyle \int \tan^{-1} x\ dx {/eq}.

Indefinite Integral:

The formula of integration that we have used in the given problem are: {eq}\int \frac{x}{x^2+1}dx=\frac{1}{2}\ln \left|x^2+1\right|+c\\ \int \frac{1}{u}du=\ln \left(\left|u\right|\right)+c\\ \int adx=ax+c\\ {/eq} Similarly, the rule that we have used are: {eq}\int \:uv'=uv-\int \:u'v\\ \int \:f\left(g\left(x\right)\right)\cdot \:g'\left(x\right)dx=\int \:f\left(u\right)du,\:\quad \:u=g\left(x\right) {/eq}

Answer and Explanation: 1

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In this question, we need to evaluate using integration by parts:

{eq}\displaystyle \int \tan^{-1} x\ dx {/eq}

So we use the ILATE rule and...

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Indefinite Integral: Definition, Rules & Examples

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Chapter 7 / Lesson 14
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Learn the concept and rules of indefinite and definite integrals, as well as how to find an indefinite integral through examples. View a table of integrals.


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