几个高数题.积分..不用完全解答..做的差不多给个思路就可以.积分.X^(1/2) * e^(X^(1/2)) dx积分.X * (sinx)^2 * cosx dx积分.1/(X + X * X^(1/2))积分.(1 + X^(1/2))^8每个题后面都有个dx..后面俩题忘写了.
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![几个高数题.积分..不用完全解答..做的差不多给个思路就可以.积分.X^(1/2) * e^(X^(1/2)) dx积分.X * (sinx)^2 * cosx dx积分.1/(X + X * X^(1/2))积分.(1 + X^(1/2))^8每个题后面都有个dx..后面俩题忘写了.](/uploads/image/z/5561040-48-0.jpg?t=%E5%87%A0%E4%B8%AA%E9%AB%98%E6%95%B0%E9%A2%98.%E7%A7%AF%E5%88%86..%E4%B8%8D%E7%94%A8%E5%AE%8C%E5%85%A8%E8%A7%A3%E7%AD%94..%E5%81%9A%E7%9A%84%E5%B7%AE%E4%B8%8D%E5%A4%9A%E7%BB%99%E4%B8%AA%E6%80%9D%E8%B7%AF%E5%B0%B1%E5%8F%AF%E4%BB%A5.%E7%A7%AF%E5%88%86.X%5E%281%2F2%29+%2A+e%5E%28X%5E%281%2F2%29%29+dx%E7%A7%AF%E5%88%86.X+%2A+%28sinx%29%5E2+%2A+cosx+dx%E7%A7%AF%E5%88%86.1%2F%28X+%2B+X+%2A+X%5E%281%2F2%29%29%E7%A7%AF%E5%88%86.%281+%2B+X%5E%281%2F2%29%29%5E8%E6%AF%8F%E4%B8%AA%E9%A2%98%E5%90%8E%E9%9D%A2%E9%83%BD%E6%9C%89%E4%B8%AAdx..%E5%90%8E%E9%9D%A2%E4%BF%A9%E9%A2%98%E5%BF%98%E5%86%99%E4%BA%86.)
几个高数题.积分..不用完全解答..做的差不多给个思路就可以.积分.X^(1/2) * e^(X^(1/2)) dx积分.X * (sinx)^2 * cosx dx积分.1/(X + X * X^(1/2))积分.(1 + X^(1/2))^8每个题后面都有个dx..后面俩题忘写了.
几个高数题.积分..
不用完全解答..做的差不多给个思路就可以.
积分.X^(1/2) * e^(X^(1/2)) dx
积分.X * (sinx)^2 * cosx dx
积分.1/(X + X * X^(1/2))
积分.(1 + X^(1/2))^8
每个题后面都有个dx..后面俩题忘写了.
几个高数题.积分..不用完全解答..做的差不多给个思路就可以.积分.X^(1/2) * e^(X^(1/2)) dx积分.X * (sinx)^2 * cosx dx积分.1/(X + X * X^(1/2))积分.(1 + X^(1/2))^8每个题后面都有个dx..后面俩题忘写了.
积分.X^(1/2) * e^(X^(1/2)) dx
x^1/2 = t,x = t^2
积分.t * e^t dt^2
= 2积分.t^2 * e^t dt
= 2积分.t^2 de^t
= 2(t^2 e^t - 积分.e^t dt^2)
= 2(t^2 e^t - 2积分.te^t dt)
= 2(t^2 e^t - 2(te^t - 积分.e^t dt))
= 2(t^2 e^t - 2(te^t - e^t))
= 2t^2 e^t - 4te^t + 4e^t
= 2x e^(x^1/2) - 4(x^1/2)e^(x^1/2) + 4e^(x^1/2) + C
cos^3(x)=(cos3x+3cosx)/4
积分.X * (sinx)^2 * cosx dx
= 积分.X * (1 - cos^2 x) * cosx dx
= 积分.xcosx dx - 积分.xcos^3 x dx
= 积分.xcosx dx - (1/4)积分.x(cos3x+3cosx) dx
= 积分.xcosx dx - (1/4)积分.xcos3x dx - (3/4)积分.xcosx dx
= (1/4)积分.xcosx dx - (1/36)积分.3xcos3x d(3x)
= (1/4)积分.xdsinx - (1/36)积分.3xcos3x d(3x)
= (1/4)(xsinx - 积分.sinx dx) - (1/36)积分.3x dsin(3x)
= (1/4)(xsinx + cosx) - (1/36)(3xsin3x-积分.sin(3x)d(3x))
= (1/4)(xsinx + cosx) - (1/36)(3xsin3x+cos(3x)) + C
积分.1/(X + X * X^(1/2)) dx
= 积分.1/(X + X^(3/2)) dx
x^1/2 = r
= 积分.2r/(r^2 + r^3) dr
= 积分.2/(r + r^2) dr
= 2积分.1/(r(r+1)) dr
= 2积分.(r+1-r)/(r(r+1)) dr
= 2(积分.(r+1)/(r(r+1)) dr - 积分.r/(r(r+1)) dr)
= 2(积分.1/r dr - 积分.1/(r+1) d(r+1))
= 2(ln|x^1/2| - ln|x^1/2+1|) + C
= 2ln|x^1/2| - 2ln|x^1/2+1| + C
= 2(ln|r| - ln|r+1|)
积分.(1 + X^(1/2))^8 dx
= 积分.(1 + x^(1/2))^8 d((x^(1/2))^2)
x^1/2 = k
= 积分.2k(1 + k)^8 d(k)
= 积分.2k(1 + k)^8 d(1+k)
= (2/9)积分.k d(1+k)^9
= (2/9)((1+k)^9 k - 积分.(1+k)^9dk)
= (2/9)((1+k)^9 k - 积分.(1+k)^9d(1+k))
= (2/9)((1+k)^9 k - (1/10)(1+k)^10) + C
= (2/9)((1+x^1/2)^9 x^1/2 - (1/10)(1+x^1/2)^10) + C
不一定对哦 我自己做的 = =.