∫(x^7+1)sin^2xdx= 求解题过程,谢谢,急等!
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Sievers分析仪
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∫(x^7+1)(sinx)^2dx
=(1/2)∫(x^7+1)(1-cos2x)dx
=(1/2)∫(x^7-1)dx-(1/2)∫(x^7+1)cos2xdx
=(1/2)∫x^7dx-(1/2)∫dx-(1/2)∫x^7cos2xdx-(1/2)∫cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)∫x^7d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x+(1/4)∫sin2xd(x^7)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x+(7/4)∫x^6sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)∫x^6d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(7/8)∫cos2xd(x^6)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/4)∫x^5cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)∫x^5d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x-(21/8)∫sin2xd(x^5)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x-(105/4)∫x^4sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)∫x^4d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/8)∫cos2xd(x^4)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/2)∫x^3cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)∫x^3d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x+(105/4)∫sin2xd(x^3)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x+(315/4)∫x^2sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)∫x^2d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)∫cos2xd(x^2)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/4)∫xcos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)∫xd(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)xsin2x-(315/8)∫sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)xsin2x+(315/16)cos2x+C
=(1/2)∫(x^7+1)(1-cos2x)dx
=(1/2)∫(x^7-1)dx-(1/2)∫(x^7+1)cos2xdx
=(1/2)∫x^7dx-(1/2)∫dx-(1/2)∫x^7cos2xdx-(1/2)∫cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)∫x^7d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x+(1/4)∫sin2xd(x^7)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x+(7/4)∫x^6sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)∫x^6d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(7/8)∫cos2xd(x^6)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/4)∫x^5cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)∫x^5d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x-(21/8)∫sin2xd(x^5)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x-(105/4)∫x^4sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)∫x^4d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/8)∫cos2xd(x^4)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/2)∫x^3cos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)∫x^3d(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x+(105/4)∫sin2xd(x^3)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x+(315/4)∫x^2sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)∫x^2d(cos2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)∫cos2xd(x^2)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/4)∫xcos2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)∫xd(sin2x)
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)xsin2x-(315/8)∫sin2xdx
=(1/16)x^8-(1/2)x-(1/4)sin2x-(1/4)x^7sin2x-(7/8)x^6cos2x
+(21/8)x^5sin2x+(105/8)x^4cos2x-(105/4)x^3sin2x-(315/8)x^2cos2x
+(315/8)xsin2x+(315/16)cos2x+C
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