帮助求一道高数不定积分的题目
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/07/16 03:27:29
帮助求一道高数不定积分的题目
∫xsinx∧4dx
∫xsinx∧4dx
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∫ xsin^4x dx = ∫ x(sin²x)² dx
= ∫ x[1/2 • (1 - cos2x)]² dx
= (1/4)∫ x(1 - 2cos2x + cos²2x) dx
= (1/4)∫ x dx - (1/2)∫ xcos2x dx + (1/8)∫ (x + xcos4x) dx
= (3/8)∫ x dx - (1/4)∫ x dsin2x + (1/32)∫ x dsin4x
= (3/8)∫ x dx - (1/4)xsin2x + (1/4)∫ sin2x dx + (1/32)xsin4x - (1/32)∫ sin4x dx
= 3x²/16 - (1/4)xsin2x - (1/8)cos2x + (1/32)xsin4x + (1/128)cos4x + C
= ∫ x[1/2 • (1 - cos2x)]² dx
= (1/4)∫ x(1 - 2cos2x + cos²2x) dx
= (1/4)∫ x dx - (1/2)∫ xcos2x dx + (1/8)∫ (x + xcos4x) dx
= (3/8)∫ x dx - (1/4)∫ x dsin2x + (1/32)∫ x dsin4x
= (3/8)∫ x dx - (1/4)xsin2x + (1/4)∫ sin2x dx + (1/32)xsin4x - (1/32)∫ sin4x dx
= 3x²/16 - (1/4)xsin2x - (1/8)cos2x + (1/32)xsin4x + (1/128)cos4x + C