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∫sin4xCos2xDx 积分

方法1: 原式=∫sin⁴x cos²x =∫sin⁴x (1 - sin²x) dx =∫(sin⁴x - sin^6x) dx = ∫sin⁴x dx - ∫sin^6x dx 后面的看附图,自己整理吧 方法2: 原式=∫sin⁴x cos²x dx =∫sin²x (sinxcosx)² dx...

如图

(sin∧4xcos∧2x)的原函数是 ∫(sin∧4xcos∧2x)dx =∫[sin^2x(sinxcosx)^2dx =1/8∫(1-cos2x)(sin2x)^2dx =1/8∫(sin2x)^2dx-1/16∫(sin2x)^2d(sin2x) =1/16∫[1-cos4x]dx-1/48(sin2x)^3 =x/16-1/64*sin4x-1/48*(sin2x)^3+C 原函数的定义 primitive f...

∫ (sin²x - cos²x)/(sin⁴x + cos⁴x) dx = ∫ [- (cos²x - sin²x)]/[(sin⁴x + 2sin²xcos²x + cos⁴x) - 2sin²xcos²x] dx = ∫ (- cos2x)/[(sin²x + cos²x)² - 2sin...

∫ cos²x dx = ∫ (1 + cos2x)/2 dx = x/2 + (1/4)sin4x + C ∫ cos³x dx = ∫ (1 - sin²x) dsinx = sinx - (1/3)sin³x + C ∫ cos⁴x dx = ∫ (cos²x)² dx = ∫ [(1 + cos2x)/2]² dx = (1/4)∫ (1 + 2cos2x + ...

①∫xsin2xdx =-0.5∫xdcos2x =-0.5xcos2x+0.5∫cos2xdx =-0.5xcos2x+0.25sin2x+C ②∫(lnx)²dx =x(lnx)²-∫ x*2lnx*(1/x)dx =x(lnx)²-2∫lnxdx =x(lnx)²-2xlnx+2∫ x*(1/x)dx =x(lnx)²-2xlnx+2x+C ③∫ 1/√(4x-x²) dx =∫ 1/...

积化和差∫sinxsin2xsin3xdx=1/2∫(cosx-cos3x)sin3xdx=1/2∫cosxsin3xdx-1/2∫cos3xsin3xdx=1/4∫(sin2x+sin4x)dx-1/4∫sin6xdx=-1/8cos2x-1/16cos4x+1/24cos6x+C数学软件验算:

∫sinx/(1+sin^4x) dx =∫dcosx/(1+(1-cos^2x)^2) =∫dcosx/(2-2cos^2x+cos^4x) =∫du/(2-2u^2+u^4) =。。。 查不定积分表 吧

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