sint+2积分

鞠舒菡2916√(1+(sinx)∧2) 的不定积分 -
卞矩婵18660669965 ______ (1+(sinx)^2)^0.5 从0到π的积分为 3.8202.

鞠舒菡2916求∫1/2+sinx的不定积分 -
卞矩婵18660669965 ______[答案] 万能代换:令y = tan(x/2),dx = 2dy/(1 + y²),sinx = 2y/(1 + y²) ∫ 1/(2 + sinx) dx = ∫ [2/(1 + y²)]/[2 + 2y/(1 + y²)] dy = ∫ 1/(y² + y + 1) dy = ∫ 1/[(y + 1/2)² + 3/4] d(y + 1/2) = (2/√3)arctan[(y + 1/2)(2√3)] + C = (2/√3)arctan[(2y + 1)/√3] + C = (2/√3)arctan[...

鞠舒菡29161 +(sinx)^2积分1/(1+sinx^2的不定积分 -
卞矩婵18660669965 ______[答案] 原式=∫[1/(sinx)^2]/[1+1/(sinx)^2]dx =-∫1/[2+(cotx)^2]d(cotx) =-(1/√2)∫1/[1+(cotx/√2)^2]d(cotx/√2) =-(1/√2)arctan(cotx/√2)+C 或者另外一种方法: 1.分子分母同时除以(cosx)^2 2.换元:原式=∫1/[1+2(tanx)^2]d(tanx)=1/2(∫1/[(1/√2)^2+(tanx)^2]d(tanx...

鞠舒菡29161/(sinx/2)的平方的积分? -
卞矩婵18660669965 ______ ∫ dx/(sin(x/2))^2 =∫ (csc(x/2))^2 dx=∫ ( 1+(cot(x/2))^2) dx= x -2csc(x/2) + C

鞠舒菡2916有理函数的积分1.∫1/(1+2sinx)dx 2.∫1/(1+tanx)dx 3.∫1/((x+1)^(1/2)+(x+1)^(1/3))dx 4.∫1/(5+4cos2x)dx 5.∫1/(sinxcosx^3)dx -
卞矩婵18660669965 ______[答案] 答:2.令tanx=t,则x=arctant,dx=dt/(1+t^2).原积分=∫1/(1+t)*1/(1+t^2) dt=1/2*∫[1/(1+t)+(1-t)/(1+t^2)] dt=1/2ln|1+t|+1/2arctant-1/4ln(1+t^2) + C=1/2ln|1+tanx|+x/2+1/2ln|cosx|+ C=1/2(x+ln|sinx+cosx|) + C...

鞠舒菡2916(1+sinx)/(1+x^2)的不定积分? -
卞矩婵18660669965 ______[答案] ∫(1+sinx)/(1+x^2)*dx =∫1/(1+x^2)*dx+∫sinx/(1+x^2)*dx =arctanx+∫sinx/(1+x^2)*dx 而∫sinx/(1+x^2)*dx求不出(原函数不能用初等函数表示) 原式无法求出

鞠舒菡29161/(1+sinx^2的不定积分 -
卞矩婵18660669965 ______[答案] 1/(1+(sinx)^2) =2/(3-cos2x)=1/(3/2-1/2cos2x) 其不定积分为: (1/根号2)*arctan[(根号2)*sin2x]/(3cos2x-1)

鞠舒菡2916一道不定积分题!求不定积分∫1/(sinx+cosx)dx 要求:用2种方法求解! -
卞矩婵18660669965 ______[答案] 解法一:万能代换! 令u=tanx/2,则sinx=2u/(1+u²),cosx=(1-u²)/(1+u²),dx=2du/(1+u²),于是得 ∫1/(sinx+cosx)=∫2/(1+2u-u²)du =√2/2∫[1/(u-(1-√2))-1/(u-(1+√2))]du =√2/2ln|(u-(1-√2))/(u-(1+√2))|+C =√2/2ln|(tanx/2-1+√2)/(tanx/2-1-√2)+C. 解法...

鞠舒菡2916关于求积分积分1/(sinx+cosx)dx -
卞矩婵18660669965 ______[答案] 令t=tan(x/2),x=2arctant, dx=[2/(1+t^2)]dt, sinx=2t/(1+t^2), cosx=(1-t^2)/(1+t^2), 积分1/(sinx+cosx)dx =积分2/(1-t^2+2t)dt =2积分1/[2-(t-1)^2]dt =-2积分1/[(t-1)^2-2]d(t-1) =-2*(1/2√2)*ln|(t-1-√2)/(t-1+√2)|+C =-1/√2*ln|(t-1-√2)/(t-1+√2)|+C (C为任意实数)

鞠舒菡2916证明:积分符号sinx/(sinx+cosx)=积分符号cosx/(sinx+cosx)在[0,π/2]相等 加急证明:积分符号sinx/(sinx+cosx)dx=积分符号cosx/(sinx+cosx)dx在[0,π/2]相等 加急 -
卞矩婵18660669965 ______[答案] 我没公式编辑器,只能这样写了 这很简单的,令x=π/2-t 带入即可, 积分符号sinx/(sinx+cosx)dx =积分符号sin(π/2-t )/(sin(π/2-t )+cos(π/2-t ))d(π/2-t ) =-cost/(cost+sint)dt 注意前面有符号,应为sin(π/2-t)=cost -cost/(cost+sint)dt 积分区间为[π/2,0] =cost/(...