arctanx 定积分上限是根号3下限是根号3/3

∫(√3/3->√3) arctanx dx
= x * arctanx |(√3/3->√3) - ∫(√3/3->√3) x * d(arctanx) √3) x/(1+x²) dx
= [√3 * π/3 - √3/3 * π/6] - (1/2)∫(√3/3->√3) 1/(1+x²) d(1+x²)
= 5π/(6√3) - (1/2)ln(1+x²) |(√3/3->√3)
= 5π/(6√3) - (1/2)[ln(1+3) - ln(1+1/3)]
= 5π/(6√3) - (1/2)ln3

分部积分法，同意楼上