Question

integration of (tan^-1 x)^3/1+x^2 from 1 to 0

Answer 1

£(tan–¹ x)³/1+x² dx

tan–1x=t

(1/1+x² )dx=dt

£t³ dt=t⁴/4=[(tan^-1 x)⁴/4] =1/4[tan^-1(1)]⁴ -1/4[tan^-1(0)]⁴=1/4(π/4)⁴ -0

=1/4(π⁴/4⁴)=π⁴/4³.

Answer 2

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