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人気の高い微分積分問題
integral of 18x^2sqrt(6x^3+5)
\int\:18x^{2}\sqrt{6x^{3}+5}dx
(\partial)/(\partial y)(6y^2)
\frac{\partial\:}{\partial\:y}(6y^{2})
integral of e^{-st}*sin(2t)
\int\:e^{-st}\cdot\:\sin(2t)dt
limit as x approaches (5pi)/2 of e^{tan(x)}
\lim\:_{x\to\:\frac{5π}{2}}(e^{\tan(x)})
面積 y=0,y=sqrt(x),y=x-2
area\:y=0,y=\sqrt{x},y=x-2
(\partial)/(\partial x)((3x-1)^2(x^3+1)^2)
\frac{\partial\:}{\partial\:x}((3x-1)^{2}(x^{3}+1)^{2})
derivative y=(x+3)^3
derivative\:y=(x+3)^{3}
(dy)/(dt)=-y/t
\frac{dy}{dt}=-\frac{y}{t}
integral of 6/(x^2-1)
\int\:\frac{6}{x^{2}-1}dx
derivative f(x)=4x^2sin(x)-7x
derivative\:f(x)=4x^{2}\sin(x)-7x
integral from 0 to 5 of 1/(sqrt(3x+1))
\int\:_{0}^{5}\frac{1}{\sqrt{3x+1}}dx
limit as x approaches-1-of (|x+1|)/(x+1)
\lim\:_{x\to\:-1-}(\frac{\left|x+1\right|}{x+1})
integral of 9(2x-9)^8
\int\:9(2x-9)^{8}dx
derivative (1+x)^n
derivative\:(1+x)^{n}
derivative of x^{2^x}
\frac{d}{dx}(x^{2^{x}})
y^{''}-(2/t)y^'+(2/(t^2))y=(2t)/(1+t^2)
y^{\prime\:\prime\:}-(\frac{2}{t})y^{\prime\:}+(\frac{2}{t^{2}})y=\frac{2t}{1+t^{2}}
integral of x^9sqrt(x^5+4)
\int\:x^{9}\sqrt{x^{5}+4}dx
d/(dy)(y^{-2})
\frac{d}{dy}(y^{-2})
derivative sqrt(x-1)
derivative\:\sqrt{x-1}
y^'=x+2y
y^{\prime\:}=x+2y
integral of (x^2+2x-1)/(x^3-x)
\int\:\frac{x^{2}+2x-1}{x^{3}-x}dx
integral of 6e^{x+2y}
\int\:6e^{x+2y}dy
y= 4/(-4x+3+3x^2)(dy)/(dx)
y=\frac{4}{-4x+3+3x^{2}}\frac{dy}{dx}
sum from n=0 to infinity of n!(2x-1)^n
\sum\:_{n=0}^{\infty\:}n!(2x-1)^{n}
(\partial)/(\partial x)(4x+3y)
\frac{\partial\:}{\partial\:x}(4x+3y)
(\partial)/(\partial x)(xyz-e^z)
\frac{\partial\:}{\partial\:x}(xyz-e^{z})
(x^2-yx^2)dy+y^2(1+x)dx=0
(x^{2}-yx^{2})dy+y^{2}(1+x)dx=0
(\partial)/(\partial t)(x+ysin(t))
\frac{\partial\:}{\partial\:t}(x+y\sin(t))
integral of t^2-9
\int\:t^{2}-9dt
integral of (3x^2+4x+2)
\int\:(3x^{2}+4x+2)dx
derivative of (48/((1-2x)^4))
\frac{d}{dx}(\frac{48}{(1-2x)^{4}})
derivative of ln(x+sqrt(2+x^2))
\frac{d}{dx}(\ln(x+\sqrt{2+x^{2}}))
xy^2y^'=x^3+y^3
xy^{2}y^{\prime\:}=x^{3}+y^{3}
integral from 0 to pi/6 of ln(sec(x))
\int\:_{0}^{\frac{π}{6}}\ln(\sec(x))dx
面積 y=sqrt(x),y=x^2,x=2
area\:y=\sqrt{x},y=x^{2},x=2
laplace変換する f(t)=t^3
laplacetransform\:f(t)=t^{3}
derivative (qx+r)/(sx+t)
derivative\:\frac{qx+r}{sx+t}
derivative of ln(x-sin(x))
\frac{d}{dx}(\ln(x)-\sin(x))
derivative (x^3+6x)/3
derivative\:\frac{x^{3}+6x}{3}
g(x)=3x-2+1/x-1/(x^2)
g(x)=3x-2+\frac{1}{x}-\frac{1}{x^{2}}
integral of x/(sqrt(2-x-x^2))
\int\:\frac{x}{\sqrt{2-x-x^{2}}}dx
xy^2(dy)/(dx)=y^3+x^3
xy^{2}\frac{dy}{dx}=y^{3}+x^{3}
inverseラプラス 1/(s(s^2+5))
inverselaplace\:\frac{1}{s(s^{2}+5)}
limit as x approaches 0 of sin(3x)
\lim\:_{x\to\:0}(\sin(3x))
limit as j approaches infinity of (2e^j+e^{-j}+2e^4+1)/(e^j+e^4)
\lim\:_{j\to\:\infty\:}(\frac{2e^{j}+e^{-j}+2e^{4}+1}{e^{j}+e^{4}})
derivative y=sec^2(sqrt(x))
derivative\:y=\sec^{2}(\sqrt{x})
limit as n approaches infinity of \sum_{i=1}^nsqrt((2i)/n)*2/n
\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}\sqrt{\frac{2i}{n}}\cdot\:\frac{2}{n})
(\partial)/(\partial x)(1/(sqrt(x+2)))
\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x+2}})
tangent f(x)=3x-4x^2,(-1,-7)
tangent\:f(x)=3x-4x^{2},(-1,-7)
integral of 5xsqrt(x+4)
\int\:5x\sqrt{x+4}dx
derivative of (1-x^{2/3})
\frac{d}{dx}((1-x)^{\frac{2}{3}})
sum from n=0 to infinity of 1/(3^n+2)
\sum\:_{n=0}^{\infty\:}\frac{1}{3^{n}+2}
integral of θcos(θ)
\int\:θ\cos(θ)dθ
integral of (x^4)/(1-x^2)
\int\:\frac{x^{4}}{1-x^{2}}dx
integral of x^2x^3
\int\:x^{2}x^{3}dx
integral of 7v(v^2+6)^2
\int\:7v(v^{2}+6)^{2}dv
面積 6x-x^3,|2*x|
area\:6x-x^{3},\left|2\cdot\:x\right|
derivative ln(16+x^2)
derivative\:\ln(16+x^{2})
limit as v approaches 1 of (v^2-5)/v
\lim\:_{v\to\:1}(\frac{v^{2}-5}{v})
limit as x approaches infinity+of 3*+2^x
\lim\:_{x\to\:\infty\:+}(3\cdot\:+2^{x})
integral of (-7x)/(\sqrt[4]{x+2)}
\int\:\frac{-7x}{\sqrt[4]{x+2}}dx
tangent x/((x+1))
tangent\:\frac{x}{(x+1)}
integral of (x^2+4)^{1/2}
\int\:(x^{2}+4)^{\frac{1}{2}}dx
integral from 0 to y of 0.125
\int\:_{0}^{y}0.125dx
limit as x approaches 1 of x^{(1/(1-x))}
\lim\:_{x\to\:1}(x^{(\frac{1}{1-x})})
sum from n=1 to infinity of n^2(2/3)^n
\sum\:_{n=1}^{\infty\:}n^{2}(\frac{2}{3})^{n}
derivative of 7x-1
\frac{d}{dx}(7x-1)
derivative of x(x-aln(x+1+b^2))
\frac{d}{dx}(x(x-a)\ln(x+1+b^{2}))
derivative of sqrt(1+x-y^2)
\frac{d}{dx}(\sqrt{1+x-y^{2}})
integral of (x^n)/(n!)
\int\:\frac{x^{n}}{n!}dx
(dy)/(dt)-y/(2t)=3t
\frac{dy}{dt}-\frac{y}{2t}=3t
limit as x approaches 0 of ln(x^2)-x^{-2}
\lim\:_{x\to\:0}(\ln(x^{2})-x^{-2})
derivative of (x^3-9x^{-1/3})
\frac{d}{dx}((x^{3}-9x)^{-\frac{1}{3}})
derivative of tan(cot(ln(x))+sec(e^x))
\frac{d}{dx}(\tan(\cot(\ln(x)))+\sec(e^{x}))
limit as x approaches 0+of (sin(x))/x
\lim\:_{x\to\:0+}(\frac{\sin(x)}{x})
(\partial)/(\partial x)(x^3yz^2+4yz)
\frac{\partial\:}{\partial\:x}(x^{3}yz^{2}+4yz)
integral of 4x^5e^{x^6}
\int\:4x^{5}e^{x^{6}}dx
(\partial)/(\partial y)(6x+10y)
\frac{\partial\:}{\partial\:y}(6x+10y)
derivative of 6(4e^{x^2}x^3+6e^{x^2}x)
\frac{d}{dx}(6(4e^{x^{2}}x^{3}+6e^{x^{2}}x))
5x^{''}+5x^'+6x=0,x^'(0)=0.45,x(0)=-0.3
5x^{\prime\:\prime\:}+5x^{\prime\:}+6x=0,x^{\prime\:}(0)=0.45,x(0)=-0.3
integral of (cos(sqrt(x)))/(sqrt(x))
\int\:\frac{\cos(\sqrt{x})}{\sqrt{x}}dx
(\partial)/(\partial x)(xz^2)
\frac{\partial\:}{\partial\:x}(xz^{2})
integral of 5/(6+5x)
\int\:\frac{5}{6+5x}dx
integral of (sqrt(1-x^2))/(x^4)
\int\:\frac{\sqrt{1-x^{2}}}{x^{4}}dx
limit as (x,y) approaches (0,0) of xy^2
\lim\:_{(x,y)\to\:(0,0)}(xy^{2})
integral of 1/(xsqrt(4x^2+9))
\int\:\frac{1}{x\sqrt{4x^{2}+9}}dx
derivative of 4sqrt(x-3)
\frac{d}{dx}(4\sqrt{x-3})
(x+2y^2)*dx+xy*dy=0
(x+2y^{2})\cdot\:dx+xy\cdot\:dy=0
integral of x/(sqrt(7x^2-3))
\int\:\frac{x}{\sqrt{7x^{2}-3}}dx
integral of (sin^2(x))
\int\:(\sin^{2}(x))dx
limit as x approaches a of f(a)
\lim\:_{x\to\:a}(f(a))
integral of 9xcos(4x)
\int\:9x\cos(4x)dx
面積 x=-2,x=2,y=x,y=x^2-2
area\:x=-2,x=2,y=x,y=x^{2}-2
y^{''}+ay-b=0
y^{\prime\:\prime\:}+ay-b=0
2x^5+3yy^'=0
2x^{5}+3yy^{\prime\:}=0
integral from-1 to 3 of (-x^2+2x+3)
\int\:_{-1}^{3}(-x^{2}+2x+3)dx
integral of 1/(e^{sqrt(x))}
\int\:\frac{1}{e^{\sqrt{x}}}dx
integral from 0 to 2 of (8ti-t^3j+4t^7k)
\int\:_{0}^{2}(8ti-t^{3}j+4t^{7}k)dt
limit as x approaches 3-of 6-x
\lim\:_{x\to\:3-}(6-x)
dy=(dx)/y
dy=\frac{dx}{y}
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