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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestGiven \(\displaystyle \int \left(\tan^{-1}(x)\right)^2dx\)

Now Let \(\tan^{-1}(x) = t\Leftrightarrow x = \tan (t)\Leftrightarrow dx = \sec^2 (t) dt\)

So \(\displaystyle \int t^2 \cdot \sec^2 (t) dt\)

Now Using Integration by parts , we get

\(\displaystyle =t^2 \tan (t)-2 \int t\cdot \tan (t)dt\)

Again using I.B.P, we get

\(\displaystyle = t^2 \cdot \tan (t)-2t\cdot \ln \left|\sec (t)\right|+2\int \ln \left|\sec (t)\right| dt\)

Now I did not understand How can i solve \(\displaystyle \int \ln \left|\sec (t)\right|dt\)

OR may be yours question is like \(\displaystyle \int_{0}^{\frac{\pi}{4}}\left(\tan^{-1}(x)\right)^2dx\)

OR \(\displaystyle \int_{0}^{\frac{\pi}{2}}\left(\tan^{-1}(x)\right)^2dx\)

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use of integration in daily life

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its tan inverse x whole square

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You mean \((arctan x)^2\), right?

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Is this \[(\arctan(x))^2\] or \[(\cot(x))^2\]

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