作业帮∫ x^3*sin^2x (x^4 2x^2 1)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 21:38:41
sin^2(x)cos^4(x)=1/4*sin²2xcos²x=1/4*(1-cos4x)/2*(1+cos2x)/2=1/16*(1+cos2x-cos4x-cos2xcos4
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[
用公式a³+b³=(a+b)(a²-ab+b²)cos^6x+sin^6x=(cos²x)³+(sin²x)³=(cos
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)
求采纳.再问：图不太清楚但谢谢啦😊
原式=-∫cos²xdcosx=-cos³x/3+C再问：第一步能讲一下为什么吗？再答：dcosx=-sinxdx采纳吧
f(x)=cos(3x)*cos(2x)+sin(3x)*sin(2x)=cos(3x-2x)=cosxf'(x)=-sinx
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
由和差化积公式分子=2sin[(x^3+x^2)/2]cos[(x^3+x^2-2x)/2]x→0,则(x^3+x^2)/2→0,sin则(x^3+x^2)/2和(x^3+x^2)/2是等价无穷小而c
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
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