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常见 微积分 问题
integral of cot^5(x/2)csc^2(x/2)
\int\:\cot^{5}(\frac{x}{2})\csc^{2}(\frac{x}{2})dx
derivative sin^2(9x)
derivative\:\sin^{2}(9x)
面积 y=28-x^2,y=0.6x,y=3x
area\:y=28-x^{2},y=0.6x,y=3x
integral of 3/(sec(x)-1)
\int\:\frac{3}{\sec(x)-1}dx
limit as x approaches a of 2f(x)
\lim\:_{x\to\:a}(2f(x))
derivative of cos(sqrt(x+1))
\frac{d}{dx}(\cos(\sqrt{x+1}))
t^2(dy)/(dt)=-y
t^{2}\frac{dy}{dt}=-y
derivative of 6xy+5x^2
\frac{d}{dx}(6xy+5x^{2})
integral of 1/((x-43)^{0.92)}
\int\:\frac{1}{(x-43)^{0.92}}dx
根 cotan(x)
roots\:co\tan(x)
f(x)=e^{2x}+2e^{2x}x
f(x)=e^{2x}+2e^{2x}x
integral of (8x+7)
\int\:(8x+7)dx
derivative f(x)=sqrt((1-x)/(1+x))
derivative\:f(x)=\sqrt{\frac{1-x}{1+x}}
tangent f(x)=sqrt(x^2+15),\at x=7
tangent\:f(x)=\sqrt{x^{2}+15},\at\:x=7
(\partial)/(\partial x)(arctan(y/x))
\frac{\partial\:}{\partial\:x}(\arctan(\frac{y}{x}))
derivative 6/(5x+3)
derivative\:\frac{6}{5x+3}
integral of 1/((x+1))
\int\:\frac{1}{(x+1)}dx
5y^'=2y
5y^{\prime\:}=2y
integral of sqrt(2x-2)
\int\:\sqrt{2x-2}dx
integral of x-2y+2
\int\:x-2y+2
limit as x approaches infinity of-2+x
\lim\:_{x\to\:\infty\:}(-2+x)
(\partial)/(\partial x)((6x-9y)/(6x+9y))
\frac{\partial\:}{\partial\:x}(\frac{6x-9y}{6x+9y})
y^'=-0.000631594*sqrt(y),y(0)=30
y^{\prime\:}=-0.000631594\cdot\:\sqrt{y},y(0)=30
sum from n=1 to infinity of n/(n^2+25)
\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+25}
(\partial)/(\partial y)(x^3+x^2y^2+y^3)
\frac{\partial\:}{\partial\:y}(x^{3}+x^{2}y^{2}+y^{3})
derivative of log_{10}(2x)
\frac{d}{dx}(\log_{10}(2x))
limit as x approaches 1.75-of arcsin(x/(1.75))
\lim\:_{x\to\:1.75-}(\arcsin(\frac{x}{1.75}))
integral of (1+e^x)/(sqrt(x+e^x))
\int\:\frac{1+e^{x}}{\sqrt{x+e^{x}}}dx
(\partial)/(\partial x)(x^{10}e^{xy})
\frac{\partial\:}{\partial\:x}(x^{10}e^{xy})
limit as x approaches 2-of (2x+8)/(x+2)
\lim\:_{x\to\:2-}(\frac{2x+8}{x+2})
derivative of (pix^2/4)
\frac{d}{dx}(\frac{πx^{2}}{4})
integral of 1/(4y^2+12y+9)
\int\:\frac{1}{4y^{2}+12y+9}dy
f(t)=(t^3)/3
f(t)=\frac{t^{3}}{3}
d/(dy)((dy)/y)
\frac{d}{dy}(\frac{dy}{y})
integral of sqrt(16-25x^2)
\int\:\sqrt{16-25x^{2}}dx
(4xy-18xy)dx+(2x^2-9x^2+1)dy=0
(4xy-18xy)dx+(2x^{2}-9x^{2}+1)dy=0
derivative of 4/5
\frac{d}{dx}(\frac{4}{5})
integral of 2x^3sqrt(x)
\int\:2x^{3}\sqrt{x}dx
derivative 7xarcsin(x)
derivative\:7x\arcsin(x)
limit as x approaches 1 of (ln(x))/(1-x)
\lim\:_{x\to\:1}(\frac{\ln(x)}{1-x})
derivative of 16-sqrt(x^2+64)
\frac{d}{dx}(16-\sqrt{x^{2}+64})
(dx)/(dt)=2x(7-x)
\frac{dx}{dt}=2x(7-x)
integral from 0 to 1 of ((x-1))/((x+1))
\int\:_{0}^{1}\frac{(x-1)}{(x+1)}dx
integral of 9x^2e^x
\int\:9x^{2}e^{x}dx
tangent x^2=e^{x-y}
tangent\:x^{2}=e^{x-y}
derivative of cos(x^7)
\frac{d}{dx}(\cos(x^{7}))
derivative of sin^3(x^4)
\frac{d}{dx}(\sin^{3}(x^{4}))
derivative 2^{x+2}
derivative\:2^{x+2}
integral of 1/(4x+8)
\int\:\frac{1}{4x+8}dx
integral of (2xln(x))/(-x^4)
\int\:\frac{2x\ln(x)}{-x^{4}}dx
(\partial)/(\partial x)(k(1+ae^{-b(x,w,t)x})(1+cos(wt)))
\frac{\partial\:}{\partial\:x}(k(1+ae^{-b(x,w,t)x})(1+\cos(wt)))
derivative of (7x+4^2)
\frac{d}{dx}((7x+4)^{2})
integral of 7/(xsqrt(4-49ln^2(x)))
\int\:\frac{7}{x\sqrt{4-49\ln^{2}(x)}}dx
integral of 3x(sqrt(5-x))
\int\:3x(\sqrt{5-x})dx
y^{''}+9y=tan(3x)
y^{\prime\:\prime\:}+9y=\tan(3x)
integral of 1/(sqrt(12x-9x^2))
\int\:\frac{1}{\sqrt{12x-9x^{2}}}dx
limit as x approaches 0 of (x^2+3x)/x
\lim\:_{x\to\:0}(\frac{x^{2}+3x}{x})
泰勒 ((1+x/2))/((1-x/2))
taylor\:\frac{(1+\frac{x}{2})}{(1-\frac{x}{2})}
(\partial)/(\partial x)(xy+xz+yz)
\frac{\partial\:}{\partial\:x}(xy+xz+yz)
derivative of 4(ln(x+1))
\frac{d}{dx}(4(\ln(x)+1))
integral of (7sin(x)+4sec(x))/(tan(x))
\int\:\frac{7\sin(x)+4\sec(x)}{\tan(x)}dx
integral of 2/(1+e^x)
\int\:\frac{2}{1+e^{x}}dx
integral from-1 to 3 of 2y-(y^2-3)
\int\:_{-1}^{3}2y-(y^{2}-3)dy
derivative of tan(x*sec(x))
\frac{d}{dx}(\tan(x)\cdot\:\sec(x))
sum from n=2 to infinity of (-2/3)^n
\sum\:_{n=2}^{\infty\:}(-\frac{2}{3})^{n}
integral of (ln(x))/((x+1)^2)
\int\:\frac{\ln(x)}{(x+1)^{2}}dx
integral from 1 to 2 of ((12)/(x^2)-1)
\int\:_{1}^{2}(\frac{12}{x^{2}}-1)dx
integral of 5x^2cos(x)
\int\:5x^{2}\cos(x)dx
integral of (x-ln(x))
\int\:(x-\ln(x))dx
inverse拉普拉斯 (s+2)/(s^2+4s+13)
inverselaplace\:\frac{s+2}{s^{2}+4s+13}
integral of 5sin^5(x)cos^{-3/2}(x)
\int\:5\sin^{5}(x)\cos^{-\frac{3}{2}}(x)dx
integral of cos^3(6x)sin^{-2}(6x)
\int\:\cos^{3}(6x)\sin^{-2}(6x)dx
tangent-x^3-5x^2+3x-1
tangent\:-x^{3}-5x^{2}+3x-1
limit as x approaches 4+of (|4-x|)/(4-x)
\lim\:_{x\to\:4+}(\frac{\left|4-x\right|}{4-x})
derivative of 256sin(8x)
\frac{d}{dx}(256\sin(8x))
sum from n=1 to infinity of 5/(3^n)
\sum\:_{n=1}^{\infty\:}\frac{5}{3^{n}}
((e^x+1)dy)/(dx)=y-ye^x
\frac{(e^{x}+1)dy}{dx}=y-ye^{x}
derivative y=(400)/x+7+1/5 x
derivative\:y=\frac{400}{x}+7+\frac{1}{5}x
limit as x approaches 4 of 2x-6
\lim\:_{x\to\:4}(2x-6)
integral from 5 to infinity of e^{-x/2}
\int\:_{5}^{\infty\:}e^{-\frac{x}{2}}dx
derivative of 2/3 x^3-4x^2+10x+6
\frac{d}{dx}(\frac{2}{3}x^{3}-4x^{2}+10x+6)
(dy)/(dx)= y/x ,y(1)=2
\frac{dy}{dx}=\frac{y}{x},y(1)=2
integral from 0 to 10 of 200-4x
\int\:_{0}^{10}200-4xdx
y^'=8xy,y(1)=1
y^{\prime\:}=8xy,y(1)=1
derivative f(x)=-0.004x^3-0.3x^2+600x-800
derivative\:f(x)=-0.004x^{3}-0.3x^{2}+600x-800
inverse拉普拉斯 1/((s+2/7)^2)*1/s
inverselaplace\:\frac{1}{(s+\frac{2}{7})^{2}}\cdot\:\frac{1}{s}
(\partial}{\partial u}(\frac{u+v)/2)
\frac{\partial\:}{\partial\:u}(\frac{u+v}{2})
integral of-(ln(x))/(x^3)
\int\:-\frac{\ln(x)}{x^{3}}dx
integral of 6cot^3(x)csc^3(x)
\int\:6\cot^{3}(x)\csc^{3}(x)dx
integral of 1/(sec(x)(1+cos(x)))
\int\:\frac{1}{\sec(x)(1+\cos(x))}dx
x4+y3sqrt(x)5+2y^'=0
x4+y3\sqrt{x}5+2y^{\prime\:}=0
derivative of e^{3x}+b
\frac{d}{dx}(e^{3x}+b)
integral of x^2sqrt(3x+3)
\int\:x^{2}\sqrt{3x+3}dx
derivative of 4x^2-x
\frac{d}{dx}(4x^{2}-x)
integral of 4x(2x^2+1)^8
\int\:4x(2x^{2}+1)^{8}dx
tangent f(x)=x^2-5,\at x=1
tangent\:f(x)=x^{2}-5,\at\:x=1
泰勒 x^3,\at 16/3
taylor\:x^{3},\at\:\frac{16}{3}
y^{''}-4y^'-5y=0,y(1)=0,y^'(1)=8
y^{\prime\:\prime\:}-4y^{\prime\:}-5y=0,y(1)=0,y^{\prime\:}(1)=8
derivative-cot(x)
derivative\:-\cot(x)
y^{''''}+2y^{''}=0
y^{\prime\:\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}=0
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