求不定积分(x^4)*sinx

Answer 1

∫x^4*sin(x)dx
=-∫x^4dcos(x)
=-cos(x)x^4+∫cos(x)dx^4
=-cos(x)x^4+∫4x³dsin(x)
=-cos(x)x^4+4x³sin(x)-∫sin(x)d(4x³)
=-cos(x)x^4+4x³sin(x)+∫12x²dcos(x)
=-cos(x)x^4+4x³sin(x)+12x²cos(x)-∫cos(x)d(12x²)
=-cos(x)x^4+4x³sin(x)+12x²cos(x)-∫24xdsin(x)
=-cos(x)x^4+4x³sin(x)+12x²cos(x)-24xsin(x)+24∫sin(x)dx
=-cos(x)x^4+4x³sin(x)+12x²cos(x)-24xsin(x)-24cos(x)+C
=4x(x²-6)sin(x)-(x^4-12x²+24)cos(x)+C