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**Integrate tan^-1 x** watch

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1. How do you integrate the following:

∫tan-1 x dx

2. by parts...
it's
∫1 . tan-1 x dx
3. Integration by parts:

u = tan-1 x ; du/dx = 1 + x²
dv/dx = 1 ; v = x

∫u(dv/dx) dx = uv - ∫v(du/dx) dx

∫tan-1 x dx = x tan-1 x - ∫ x/(1+x²) dx

2x = d/dx (1+x²) ∴ ∫ x/(1+x²) dx = ½ln |1+x²| + k

∫tan-1 x dx = x tan-1 x - ½ln (1+x²) + k
4. thanks boys
5. y = arctanx
tany = x
∫tany.dx - ∫x.dx

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Updated: January 26, 2006
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