∫x^3sin^2x x^4 x^2 1

附图回答:

2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1=-(1-2sin^2[(π/4)+x)-√3cos2x=-cos(π/2+2x)-√3cos2x=sin2x-√3cos2x=2[

伤心地哭开心地笑兴奋地说高兴地唱坚持地做跑跳呆呆地想傻傻地看

用公式a³+b³=(a+b)(a²-ab+b²)cos^6x+sin^6x=(cos²x)³+(sin²x)³=(cos

(2x+3)(x-4)-(x+2)(x-3)=x^2+6(2x^2-5x-12)-(x^2-x-6)=x^2+62x^2-5x-12-x^2+x+6=x^2+6-4x-12=04x=-12x=-3

0,到根号3,与-根号3到0的积分互为相反数,加起来=0

∫sin^4(x)cos^3(x)dx=∫sin^4(x)cos^2(x)cosxdx=∫sin^4(x)*[1-sin^2(x)]d(sinx)=∫sin^4(x)d(sinx)-∫sin^6(x)

方程左边1/(xx+x)+1/(xx+3x+2)+1/(xx+5x+6)+1/(xx+7x+12)+1/(xx+9x+20)对分母因式分解得1/x（x+1)+1/（x+1）(x+2)+1/(x+2)(

确实没有好的办法,只能用尝试法了.A1有三个候选数2、4、5,使用NakedQuads方法,去除了一个候选数5,剩下候选数2、4尝试在A1填入2,最后无解尝试在A1填入4,得到最终解*--------

I=1/3∫sin(4x)d(e^(3x))=1/3(sin(4x)e^(3x)-∫e^(3x)dsin(4x))=1/3sin(4x)e^(3x)-4/9∫cos(4x)de^(3x)=1/3sin

x=0:0.1:2*pi;s=2*sin(x)-sin(2*x)+2/3*sin(3*x)-1/2*sin(4*x)+2/5*sin(5*x);plot(x,s)

f(x)=sin^2x+2√3sinxcosx+sin(x+π/4)sin(x-π/4)=(1-cos2x)/2+√3sin2x+(1/2)2sin(x-π/4)cos(x-π/4)=2-2cos2x

sin^4x-sin^2xcos^2x+cos^4x=sin^4x+2sin^2xcos^2x+cos^4x-3sin^2xcos^2x=(sin^2x+cos^2x)^2-3sin^2xcos^2x

换元法?没必要啊显然这是个奇函数而积分限关于原点对称所以原式=0

xx+yy+4x-6y+13=0整理得：(x+2)^2+(y-3)^2=0那么只有(x+2)=0(y-3)=0x=-2y=3(x^2-2x)/(x^2+3y^2)=(4+4)/(4+3*9)=8/31

1、sinx=2分之根号2,或者cos(4x)=02、sinx=负二分之一,或者cosx=二分之一,或者cosx=0

sin^2(x)+cos^2(x+30)+sin(x)cos(x+30）=sin^2(x)+cos(x+30)[cos(x+30)+sinx]=sin^2(x)+cos(x+30)(cosxcos30

（1）原式=1/2∫sin√（x²+4）/（√（x²+4）d（x²+4）=-∫sin√（x²+4）d√（x²+4）=cos√（x²+4）+C

原式=∫dx/(cos²x(1+4tan²x))=∫d(tanx)/(1+4tan²x)=1/2∫d(2tanx)/(1+(2tanx)²)=arctan(2t

sin^4x-sin^2xcos^2x+cos^4x=sin^4x+2sin^2xcos^2x+cos^4x-3sin^2xcos^2x=(sin^2x+cos^2x)^2-3sin^2xcos^2x