立方根tln(t^2+1)

∫ ln(3t? + 1) dt

= tln(3t? + 1) - ∫ t * 6t/(3t? + 1) dt

= tln(3t? + 1) - 2∫ (3t? + 1 - 1)/(3t? + 1) dt

= tln(3t? + 1) - 2∫ [1 - 1/(3t? + 1)] dt

= tln(3t? + 1) - 2t + (2/√3)arctan(√3t) + C

∫(0→x) ln(3t? + 1) dt

= xln(3x? + 1) - 2x + (2/√3)arctan(√3x)

求导的话就更简单：d/dx ∫(0→x) ln(3t? + 1) dt = ln(3x? + 1)