∫sin^6(x)dx =3/4*1/2*π/2 0-π/2的定积分计算sin^6 在0到π/2 上积分 为什么等于 5/6*3/4*1/2*π/2 怎么证明?

∫sin(6x)sin(2x)dx=? 求下列不定积分.求详解（1）∫[(cos 2x)／(cos x﹢sin x)]dx; (2) ∫cot²xdx; (3) ∫{(1+2x²)／[x²(1+x²)]}dx; (4) ∫sin²(x／2)dx; (5) ∫[(cos2x)／(sin²xcos²x)]dx; (6) ∫[e^(x-4)]dx;求解 用换元法求下列积分∫x^3sin^x/(x^4+1)dx∫x^3sin^2x/(x^4+1)dx ∫cos^4x/sin^3x dx=? ∫sin(3x)cos(4x)dx= ∫[1/(sin^2(x)cos^4(x)]dx 求解∫1/(cos^4(x)sin^2(x))dx ∫sin^3(x)cos^2(x)dx= ∫sin（6x）sin（4x）dx ∫sin^2x/(1+sin^2x )dx求解, ∫(2/sin^2x)dx= ∫sinxcosx/(1+sin^4x)dx ∫1/sin^4x dx ∫(1-sin^2( x/2))dx ∫ 4/sin^2x dx ∫sin^3(x)dx=? ∫（1-sin^3x）dx ∫sin(3x-1)dx