Integrate: ∫tan-1 x dx – InterviewSolution

1.

Integrate: ∫tan-1 x dx

Answer»

∫tan^-1 x dx

= ∫1.tan^-1 x dx

= tan^-1 x∫1. dx - ∫1/(1 + x²)x dx

= x tan^-1 x - (1/2)∫2x/(1 + x²) dx

= x tan^-1 x - (1/2)log(1 + x²) + k

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