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常见 微积分 问题
integral of (x^3)/3 e^{x^2}
\int\:\frac{x^{3}}{3}e^{x^{2}}dx
derivative of 30sqrt(x)
\frac{d}{dx}(30\sqrt{x})
integral of (x^3+3x+8)e^x
\int\:(x^{3}+3x+8)e^{x}dx
limit as x approaches-infinity of x^6e^x
\lim\:_{x\to\:-\infty\:}(x^{6}e^{x})
derivative of ln(e^{-x})
\frac{d}{dx}(\ln(e^{-x}))
inverse拉普拉斯 1/(s+1)
inverselaplace\:\frac{1}{s+1}
integral of (y-2)/(y(y-4)(y+3))
\int\:\frac{y-2}{y(y-4)(y+3)}dy
derivative ((x^2-4))/x
derivative\:\frac{(x^{2}-4)}{x}
derivative of (ln(x+1)2-e^{x^2})
\frac{d}{dx}((\ln(x+1))2-e^{x^{2}})
integral of 2/(4+x^2)
\int\:\frac{2}{4+x^{2}}dx
面积 y= 1/(sqrt(x)),y=x,y=2
area\:y=\frac{1}{\sqrt{x}},y=x,y=2
integral of 2^xln(2)
\int\:2^{x}\ln(2)dx
integral of xye^z
\int\:xye^{z}dz
(dy)/(dx)=k(y-80)
\frac{dy}{dx}=k(y-80)
展开 x^2(x^2-4)
expand\:x^{2}(x^{2}-4)
integral of (7+x^7)^6x^6
\int\:(7+x^{7})^{6}x^{6}dx
integral of (3sqrt(x))/(x+9)
\int\:\frac{3\sqrt{x}}{x+9}dx
x^2y^'=2y-2xy
x^{2}y^{\prime\:}=2y-2xy
limit as x approaches 6 of 2/((x-6)^2)
\lim\:_{x\to\:6}(\frac{2}{(x-6)^{2}})
integral of 7tsin(t)cos(t)
\int\:7t\sin(t)\cos(t)dt
integral of (x+11)/(x^2-2x-15)
\int\:\frac{x+11}{x^{2}-2x-15}dx
integral of cos(10θ)
\int\:\cos(10θ)dθ
tangent f(x)=sqrt(x),\at x=81
tangent\:f(x)=\sqrt{x},\at\:x=81
泰勒 (ln(1+x^2))/x
taylor\:\frac{\ln(1+x^{2})}{x}
(\partial)/(\partial x)(2ycos(x))
\frac{\partial\:}{\partial\:x}(2y\cos(x))
integral of x^3*e^{-2x}
\int\:x^{3}\cdot\:e^{-2x}dx
integral from 0 to 2.5 of 80x
\int\:_{0}^{2.5}80xdx
integral of 9sin^3(xco)s^5x
\int\:9\sin^{3}(xco)s^{5}xdx
integral of-1/(sec^2(x))
\int\:-\frac{1}{\sec^{2}(x)}dx
integral of x/((x^2+3)^2)
\int\:\frac{x}{(x^{2}+3)^{2}}dx
tangent f(x)=12x-1.86x^2,\at x=a
tangent\:f(x)=12x-1.86x^{2},\at\:x=a
derivative y=(3x+1)sqrt(8x-1)
derivative\:y=(3x+1)\sqrt{8x-1}
(dy)/(dx)=xsqrt(y)
\frac{dy}{dx}=x\sqrt{y}
limit as x approaches infinity of 5x+2
\lim\:_{x\to\:\infty\:}(5x+2)
derivative of y= 1/((8x-5)^5)
\frac{d}{dx}y=\frac{1}{(8x-5)^{5}}
y^'-2y=4x
y^{\prime\:}-2y=4x
integral of ((1+cos(x)))/(x+sin(x))
\int\:\frac{(1+\cos(x))}{x+\sin(x)}dx
d/(dθ)(cos(2θ)cos(θ))
\frac{d}{dθ}(\cos(2θ)\cos(θ))
derivative \sqrt[5]{x^3}-8/x
derivative\:\sqrt[5]{x^{3}}-\frac{8}{x}
integral of (-6sec(x)tan(x)-7sec^2(x))
\int\:(-6\sec(x)\tan(x)-7\sec^{2}(x))dx
derivative \sqrt[4]{t}
derivative\:\sqrt[4]{t}
derivative ln(x^2+5)
derivative\:\ln(x^{2}+5)
limit as x approaches 0 of (1+3/(x^4))^x
\lim\:_{x\to\:0}((1+\frac{3}{x^{4}})^{x})
derivative of x^4-6x-9
\frac{d}{dx}(x^{4}-6x-9)
xy^'-3y^'-(x-3)cos(x)+y=0
xy^{\prime\:}-3y^{\prime\:}-(x-3)\cos(x)+y=0
integral of (e^{sqrt(t)})/(sqrt(t))
\int\:\frac{e^{\sqrt{t}}}{\sqrt{t}}dt
integral of (x^3)/(\sqrt[4]{3+x^4)}
\int\:\frac{x^{3}}{\sqrt[4]{3+x^{4}}}dx
derivative of sqrt(|x^2-6x+5|)
\frac{d}{dx}(\sqrt{\left|x^{2}-6x+5\right|})
integral from 0 to 1 of 1/(x^5)
\int\:_{0}^{1}\frac{1}{x^{5}}dx
5t(dy)/(dt)+y=t^4
5t\frac{dy}{dt}+y=t^{4}
limit as h approaches 0 of (ln(e+h)-1)/h
\lim\:_{h\to\:0}(\frac{\ln(e+h)-1}{h})
derivative of 3x^2+2/x-1/(x^2)
\frac{d}{dx}(3x^{2}+\frac{2}{x}-\frac{1}{x^{2}})
integral from 1 to e of (-2ln(x))/(x^2)
\int\:_{1}^{e}\frac{-2\ln(x)}{x^{2}}dx
integral of x/(1+sin(x))
\int\:\frac{x}{1+\sin(x)}dx
tangent f(x)= 1/5 x^{10}-1/3 x^6-x+9
tangent\:f(x)=\frac{1}{5}x^{10}-\frac{1}{3}x^{6}-x+9
integral of (2y)/((2+3y^2)^3)
\int\:\frac{2y}{(2+3y^{2})^{3}}dy
(dy)/(dt)=y-y^2
\frac{dy}{dt}=y-y^{2}
limit as x approaches-1 of-x^3+x^2-2
\lim\:_{x\to\:-1}(-x^{3}+x^{2}-2)
integral of \sqrt[6]{x^5}
\int\:\sqrt[6]{x^{5}}dx
derivative of 8e^{-4x}
\frac{d}{dx}(8e^{-4x})
derivative f(x)=8x^4tan(x)
derivative\:f(x)=8x^{4}\tan(x)
limit as x approaches 1 of ln(x+1)
\lim\:_{x\to\:1}(\ln(x+1))
d/(dy)(1/2 ln(x^2+y^2))
\frac{d}{dy}(\frac{1}{2}\ln(x^{2}+y^{2}))
sum from n=1 to infinity}(2^nx^{2n of)/(3^{n+1)}
\sum\:_{n=1}^{\infty\:}\frac{2^{n}x^{2n}}{3^{n+1}}
(\partial)/(\partial x)(4arctan(3/x))
\frac{\partial\:}{\partial\:x}(4\arctan(\frac{3}{x}))
tangent f(x)=4+5x^2,(0,4)
tangent\:f(x)=4+5x^{2},(0,4)
y^{''}+2y^'+5y=8sin(2t)
y^{\prime\:\prime\:}+2y^{\prime\:}+5y=8\sin(2t)
(\partial)/(\partial x)(ycos(x)+2xe^y)
\frac{\partial\:}{\partial\:x}(y\cos(x)+2xe^{y})
integral from 0 to 25 of 1/(sqrt(25-x))
\int\:_{0}^{25}\frac{1}{\sqrt{25-x}}dx
integral of 12xe^{6x}
\int\:12xe^{6x}dx
(\partial)/(\partial y)(xe^y+y)
\frac{\partial\:}{\partial\:y}(xe^{y}+y)
(dy)/(dx)=xy^{1/2}
\frac{dy}{dx}=xy^{\frac{1}{2}}
derivative of 2ln(2)
\frac{d}{dx}(2\ln(2))
integral of ((x^2-25)^{3/2})/(x^6)
\int\:\frac{(x^{2}-25)^{\frac{3}{2}}}{x^{6}}dx
derivative (6(x^4-2))/(x^3)
derivative\:\frac{6(x^{4}-2)}{x^{3}}
derivative (5x^2+8)^8
derivative\:(5x^{2}+8)^{8}
面积 x-1,2,5
area\:x-1,2,5
limit as x approaches 6 of (24)/x+x^2
\lim\:_{x\to\:6}(\frac{24}{x}+x^{2})
x^2*(dy)/(dx)+x(x+2)y=e^x
x^{2}\cdot\:\frac{dy}{dx}+x(x+2)y=e^{x}
integral of x^2-e^{-x}
\int\:x^{2}-e^{-x}dx
derivative of-pi^2cos(pix)
\frac{d}{dx}(-π^{2}\cos(πx))
derivative f(x)=(6-x^2)/(sqrt(x))
derivative\:f(x)=\frac{6-x^{2}}{\sqrt{x}}
d/(dt)(2e^{-t})
\frac{d}{dt}(2e^{-t})
(\partial)/(\partial x)(y^4cos(5x)*5)
\frac{\partial\:}{\partial\:x}(y^{4}\cos(5x)\cdot\:5)
integral from 0 to 5/8 of 1/((64x^2+1)^{3/2)}
\int\:_{0}^{\frac{5}{8}}\frac{1}{(64x^{2}+1)^{\frac{3}{2}}}dx
(dy)/(dx)=(3e^x)/(y^2)
\frac{dy}{dx}=\frac{3e^{x}}{y^{2}}
laplace变换 e^{-t}*(cos(4t)-2sin(4t))
laplacetransform\:e^{-t}\cdot\:(\cos(4t)-2\sin(4t))
sum from n=3 to infinity of 1/(n^2)
\sum\:_{n=3}^{\infty\:}\frac{1}{n^{2}}
derivative F(x)=5x^5(x^3-9x)
derivative\:F(x)=5x^{5}(x^{3}-9x)
limit as x approaches infinity of (2x+1)/2
\lim\:_{x\to\:\infty\:}(\frac{2x+1}{2})
derivative of (2+(x^2+1^4)^3)
\frac{d}{dx}((2+(x^{2}+1)^{4})^{3})
integral of sin(2x)cos(6x)
\int\:\sin(2x)\cos(6x)dx
integral of 2xsin(4x)
\int\:2x\sin(4x)dx
limit as x approaches infinity of (x)^2
\lim\:_{x\to\:\infty\:}((x)^{2})
derivative of (x-22/(sqrt(x)-\sqrt{22)})
\frac{d}{dx}(\frac{x-22}{\sqrt{x}-\sqrt{22}})
(\partial)/(\partial x)(a/x)
\frac{\partial\:}{\partial\:x}(\frac{a}{x})
d/(dy)((x^2y)/(x^2+y^2))
\frac{d}{dy}(\frac{x^{2}y}{x^{2}+y^{2}})
derivative of arcsin(x+log_{4}(x))
\frac{d}{dx}(\arcsin(x+\log_{4}(x)))
derivative 2t+4/3 t^{3/2}+(t^2)/2
derivative\:2t+\frac{4}{3}t^{\frac{3}{2}}+\frac{t^{2}}{2}
integral from 0 to 2 of 1/(1+x)
\int\:_{0}^{2}\frac{1}{1+x}dx
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