∫(x^2)(cosx^3)(sinx)dx

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∫(x^2)(cosx^3)(sinx)dx
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∫(x^2)(cosx^3)(sinx)dx
∫(x^2)(cosx^3)(sinx)dx

∫(x^2)(cosx^3)(sinx)dx
K = ∫ x² * cos³x * sinx dx
= ∫ x² * cos²x * (1/2)sin2x dx
= ∫ x² * (1 + cos2x)/2 * (1/2)sin2x dx
= (1/4)∫ x²sin2x dx + (1/4)∫ x²sin2xcos2x dx
= (1/4)∫ x²sin2x dx + (1/8)∫ x²sin4x dx
= (1/4)N + (1/8)M
N = ∫ x²sin2x dx
= (- 1/2)∫ x² d(cos2x)
= (- 1/2)x²cos2x + (1/2)∫ 2xcos2x dx
= (- 1/2)x²cos2x + (1/2)∫ x d(sin2x)
= (- 1/2)x²cos2x + (1/2)xsin2x - (1/2)∫ sin2x dx
= (- 1/2)x²cos2x + (1/2)xsin2x + (1/4)cos2x
M = ∫ x²sin4x dx
= (- 1/4)∫ x² d(cos4x)
= (- 1/4)x²cos4x + (1/4)∫ 2xcos4x dx
= (- 1/4)x²cos4x + (1/8)∫ x d(sin4x)
= (- 1/4)x²cos4x + (1/8)xsin4x - (1/8)∫ sin4x dx
= (- 1/4)x²cos4x + (1/8)xsin4x + (1/32)cos4x + C
所以K =
(- 1/8)x²cos2x + (1/8)xsin2x + (1/16)cos2x - (1/32)x²cos4x + (1/64)xsin4x + (1/256)cos4x + C

∫(x^2)(cosx^3)(sinx)dx sinx+cosx/sinx-cosx=2 求sinx/cos^3x +cosx/sin^3x ∫（e^sinx）*x*(cosx)^3-sinx/(cosx)^2 dx 3sinx-2cosx=0 (1)(cosx-sinx)/(cosx+sinx)+(cosx+sinx)/(cosx-sinx) (2)sin^2 x-2sinxcosx+4cos^2 x ∫x^2 sinx cosx dx .. ∫sinx/(cosx-sin^2x)dx 求∫sinx dx/(sinx+cosx)的积分,x/2-ln|sinx+cosx|+c [∫d(sinx/x)]'等于多少a、sinx/x b、sinx/x +c c、(x*cosx-cosx)/x^2 d、(x*cosx-sinx)/x^2 赶快∫【-π,π】[sinx/(x^2+cosx)]dx和∫【-π/4,-π/3】(sinx+cosx)dx求解 已知sinx+cosx/sinx-cosx=3,求tanx,2sin^2x+(sinx-cosx)^2的值 已知向量m=(2sinx,cosx-sinx),n=(根号3cosx,cosx+sinx),F(x)=m.n 已知(sinx+cosx)/(sinx-cosx)=3,求tanx,2sin²x+(sinx-cosx)²的值 (sin^x/sinx-cosx)-sinx+cosx/tan^2x-1 为什么∫( sinx)^3 (cosx)^2dx = −∫(1 −(cosx)^2(cosx)^2d( cos x) 求不定积分：1.∫e^(sinx)[x(cosx)^3-sinx]/(cosx)^2dx 2.∫[e^(3x)+e^x]/[e^(4x)-e^(2x)+1]dx (sinx+3cosx)/(3cosx-sinx)=5,则sin^2x-sinxcosx的值是 设（2cosx-sinx）（sinx+cosx+3）=0,则sec^2x= 设(2cosx-sinx)(sinx+cosx-3)=0则cos^2x=