>>372, 385
　∫x･arctan(√x)dx = (1/2)(x^2 -1)arctan(√x) - (1/4)∫(x^2 -1)/{(x+1)√x} dx
　　 = (1/2)(x^2 -1)arctan(√x) - (1/4)∫{(x-1)/√x} dx
　　 = (1/2)(x^2 -1)arctan(√x) - (1/6)x^(3/2) + (1/2)√x +c.
∴ ∫[1,3] x･arctan(√x)dx = (4π-1)/3.


>404
　e^(2x) =u とおく。
　∫e^(2x)/{e^(2x) +1}^2 dx = (1/2)∫ 1/(u+1)^2 du = -1/{2(u+1)} +c = (u-1)/{4(u+1)} +c' = (1/4)tanh(x) +c'.
　∫e^(2x)/{e^(2x) -1}^2 dx = (1/2)∫ 1/(u-1)^2 du = -1/{2(u-1)} +c = -(u+1)/{4(u-1)} +c' = -(1/4)coth(x) +c'.