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∫cosx^3dx
∫
secx dx = ln|secx + tanx| + C高数,看不懂,能不能给我解释下_百度...
答:
左边=∫dx/cosx=
∫cosx
dx/(cosx)^2 =∫d(sinx)/[1-(sinx)^2]令t=sinx,=∫dt/(1-t^2)=(1/2)∫dt/(1+t)+(1/2)∫dt/(1-t)=(1/2)∫d(1+t)/(1+t)-(1/2)∫d(1-t)/(1-t)=(1/2)ln|1+t|-(1/2)ln|1-t|+C =(1/2)ln|(1+t)/(1-t)|+C =(1/2)...
sin^3x的不定积分(cos3xsin3x的不定积分)
答:
sin^3x的不定积分为:1/3cos^3-cosx+C。解:∫sin
^3dx
=∫sin^2*sinxdx=∫)d=∫-1)dcosx=∫cos^2dcosx-∫1dcosx=1/3cos^3-cosx+C。不定积分公式:
∫cosx
dx=sinx+C、∫sinxdx=-cosx+C、∫cscxdx=-cotx+C、∫2dx=2x+C。积分中常见形式:求含有e^x的函数的积分∫x*e^xdx=∫xd...
函数f(x)=(sinx)
^3
,求定积分值
答:
=1/3 *∫ x d(cosx)^3 = x/3 *(cosx)^3 -∫1/3 *(cosx)
^3dx
= x/3 *(cosx)^3 -∫1/3 *(cosx)^2 d(sinx)= x/3 *(cosx)^3 -∫1/3 -(sinx)^2 /3 d(sinx)= x/3 *(cosx)^3 -1/3 *sinx +1/9 *(sinx)^3 ∫-x d(cosx)= -x *cosx +
∫cosx
dx = ...
积分号(x
cosx
)/(sinx)
^3dx
答:
∫x
cosx
/(sinx)
^3 dx
= ∫x/(sinx)^3 d(sinx)=-x/2·1/(sinx)^2+1/2 ∫1/(sinx)^2dx =-x/[2(sinx)^2]+1/2·∫(cscx)^2dx =-x/[2(sinx)^2]-(cotx)/2+C
x*(sinx)
^3
的积分原函数是什么
答:
=x[(
cosx
)^3/3-cosx]-∫[(cosx)^3/3-cosx]dx =x[(cosx)^3/3-cosx]+sinx -(1/3)∫(cosx)
^3dx
=x[(cosx)^3/3-cosx]+sinx -(1/3)∫[1-(sinx)^2]dsinx =x[(cosx)^3/3-cosx]+sinx -(1/3)[sinx-(sinx)^3/3]=(2/3)sinx-xcosx+(1/3)x(cosx)^3+(1/9)(...
(sinx)^3+(
cosx
)^3求积分
答:
方便起见,积分符号写成J J[(sinx)^3+(
cosx
)^3]dx=J(sinx)
^3dx
+J(cosx)^3dx=-J(1-cos^2x)dcosx+J(1-sin^2x)dsinx=-cosx-(cosx)^3/3+sinx-(sinx)^3/3+C
∫
xsin^3xdx上限π下限0求定积分
答:
而显然 ∫x*(cosx)^2d(cosx)=1/3*∫xd(cosx)^3 =x/3*(cosx)^3-∫1/3*(cosx)
^3dx
=x/3*(cosx)^3-∫1/3*(cosx)^2d(sinx)=x/3*(cosx)^3-∫1/3-(sinx)^2/3d(sinx)=x/3*(cosx)^3-1/3*sinx+1/9*(sinx)^3 ∫-xd(cosx)=-x*cosx+
∫cosx
dx =-x*cosx+sinx 二者...
∫
(0,pai) x(sinx)
^3dx
=?
答:
设f(sinx) = sin³x 则∫(0~π) xsin³x dx = ∫(0~π) xf(sinx) dx = (π/2)∫(0~π) f(sinx) dx = (π/2)∫(0~π) sin³x dx = (π/2)∫(0~π) (cos²x - 1) d
cosx
= (π/2)[(1/3)cos³x - cosx] |(0~π)= (π/2)[...
∫
dx/(sin³x
cosx
)
答:
=∫[(sinx)^2+(cosx)^2]/[(sinx)^3cosx]dx =∫1/(sinxcosx)dx+
∫cosx
/(sinx)
^3dx
=2∫1/(2sinxcosx)dx+∫1/(sinx)^3d(sinx)=2∫1/sin2x dx+∫1/(sinx)^3d(sinx)=∫1/sin2x d(2x)+∫1/(sinx)^3d(sinx)=ln|tanx|-(1/2)(sinx)^(-2)+C ...
如何求积分
∫
(secx)
^3dx
?
答:
a ≠ -1 3、∫ 1/x dx = ln|x| + C 4、∫ a^x dx = (1/lna)a^x + C,其中a > 0 且 a ≠ 1 5、∫ e^x dx = e^x + C 6、
∫ cosx
dx = sinx + C 7、∫ sinx dx = - cosx + C 8、∫ cotx dx = ln|sinx| + C = - ln|cscx| + C ...
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