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∫cos3xcos2xdx
∫cosx
cos2xcos3xdx
答:
= (1/2)cos2xcos4x + (1/2)cos²2x = (1/2)(1/2)[cos(2x + 4x) + cos(2x - 4x)] + (1/2)(1/2)(1 + cos4x)= (1/4)cos6x + (1/4)cos2x + 1/4 + (1/4)cos4x ∫ cosxcos2x
cos3x
dx = (1/4)∫ dx + (1/4)
∫ cos2x dx
+ (1/4)∫ cos4x ...
积分号
cos
的3次方乘以x乘以
dx
答:
∫cos^3 x dx =∫cosxcos^
2xdx
=∫cosx(1-sin^2)dx =∫cosxdx-∫cosxsin^2xdx =-sinx-1/2∫sin2xsinxdx =-sinx-1/2∫(-1/2(cos(3x)-cosx)dx =-sinx+1/4∫cos3xdx-1/4∫cosxdx =-sinx+1/4*1/3
∫cos3x
d3x+1/4sinx =-3/4sinx-1/12sin3x+c ...
∫cos3xcos
x
dx
答:
根据积化和差公式,
cos3x
cosx=(1/2)(cos2x+cos4x)原式=(1/2)∫(cos2x+cos4x)
dx
=(1/2)
∫cos2x
d(2x)/2+(1/2)∫cos4x d(4x)/4=(1/4)sin2x+(1/8)sin4x+C进一步化简就是:=(1/2)sinxcosx+(1/2)sinxcosxcos2x+C=(1/2)sinxc...
cosxcox
2x
cox
3xdx
的不定积分
答:
∫cosxcos2x
cos3x
dx=(1/2)∫(cosx+cos3x)
cos3xdx
=(1/2)∫cosxcos3xdx+(1/2)∫(cos3x)^2dx=(1/4)∫(cos2x+cos4x)dx+(1/4)∫(1+cos6x)dx=(1/4)
∫dx
+(1/4)
∫cos2xdx
+(1/4)∫cos4xdx...
不定积分!
答:
cos(A-B)=cosA.cosB+sinA.sinB (1)cos(A+B)=cosA.cosB-sinA.sinB (2)(1)+(2)cosA.cosB =(1/2)[cos(A-B)+cos(A+B)]=> cos3x.cos5x =(1/2)(
cos2x
+cos8x)
∫ cos3x
.cos5x
dx
=(1/2)∫ (cos2x+cos8x) dx =(1/4)sin2x +(1/16)sin8x +C ...
y’’=
cos2xcos3x
求通解
答:
∵y″=
cos2xcos3x
=(1/2)(cosx+cos5x),∴y′=(1/2)∫cosxdx+(1/2)
∫cos
5xdx=(1/2)sinx+(1/10)sin5x+A,∴y=(1/2)∫sinxdx+(1/10)∫sin5
xdx
+A
∫dx
=-(1/2)cosx-(1/50)cos5x+Ax+B。∴原微分方程的通解是:y=-(1/2)cosx-(1/50)...
求不定积分
∫
e^
3xcos2xdx
∫arccotxdx
答:
= (1/3) (
cos3x
) e^(3x) +(2/3)∫ (sin2x)e^(3x)dx = (1/3) (cos3x) e^(3x) +(2/9)∫ (sin2x)de^(3x)=(1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) - (4/9)∫ (cos2x)e^(3x) dx (13/9)∫e^
3xcos2xdx
= (1/3) (cos3x) e^(3x) +(2/9)...
x²
cos3xdx
不定积分?
答:
∫ x^2.cos3x dx =(1/3)∫ x^2 dsin3x =(1/3)x^2. sin3x -(2/3)∫ xsin3
x dx
=(1/3)x^2. sin3x +(2/9)∫ x dcos3x =(1/3)x^2. sin3x +(2/9)
xcos
3x -(2/9)
∫ cos3x
dx =(1/3)x^2. sin3x +(2/9)xcos3x +(2/27)sin3x + C ...
急急急!!!求cosx
cos2x
的不定积分
答:
楼上的用了积化和差公式,记忆不好的话容易出错。这里可以考虑用倍角公式,即
cos2x
=1-2(sinx)^2 所以,原式=∫cosx[1-2(sinx)^2]
dx
=∫cosxdx-2∫cosx(sinx)^2dx(对最右边的积分使用凑微分法)=sinx-2∫(sinx)^2d(sinx)=sinx-(2/3)(sinx)^3+C ...
(5).高数,不定积分,又蒙了,赶紧帮忙啦,最好图片哦。
答:
∫e^
3xcos2xdx
=(1/3)
∫cos
2xde^(3x)= (1/3) (
cos3x
) e^(3x) +(2/3)∫ (sin2x)e^(3x)dx = (1/3) (cos3x) e^(3x) +(2/9)∫ (sin2x)de^(3x)=(1/3) (cos3x) e^(3x) +(2/9)(sin2x)e^(3x) - (4/9)∫ (cos2x)e^(3x) dx (13/9)∫e^3xcos2xdx ...
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