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Integrate the function tan^(-1)x...

Integrate the function `tan^(-1)x`

Text Solution

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It is known that
`(d(tan^(-1)x))/dx = 1/(1 + x^2)`
using partition by parts,
Here `u = tan^(-1)x, v = 1`
`=>∫ tan^(-1)x dx `
`=> ∫ (tan^(-1)x × 1) dx`
`=> x tan^(-1)x – ∫x/(1+x^2) dx `
`=> x tan^(-1)x – ½ ∫2x/(1+x^2) dx ----- (1)`
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