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Popular Calculus Problems

(\partial)/(\partial x)(sqrt(x-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x-y^{2}})
limit as x approaches 0 of 3^x	\lim\:_{x\to\:0}(3^{x})
integral of x^3sqrt(7+x^4)	\int\:x^{3}\sqrt{7+x^{4}}dx
area x^6,x^7	area\:x^{6},x^{7}
y^{''}-2y^'+y=e^{2x}	y^{\prime\:\prime\:}-2y^{\prime\:}+y=e^{2x}
integral from 0 to ln(19) of xe^x	\int\:_{0}^{\ln(19)}xe^{x}dx
(\partial)/(\partial x)(cot(x))	\frac{\partial\:}{\partial\:x}(\cot(x))
tangent of 5/(sqrt(x))	tangent\:\frac{5}{\sqrt{x}}
derivative of 1/((x-6^2))	\frac{d}{dx}(\frac{1}{(x-6)^{2}})
tangent of f(x)=x^2+3x+4pi,\at x=2.5	tangent\:f(x)=x^{2}+3x+4π,\at\:x=2.5
(\partial)/(\partial y)(2sin(x)+sin(x+y))	\frac{\partial\:}{\partial\:y}(2\sin(x)+\sin(x+y))
limit as x approaches 0 of ((0))/x	\lim\:_{x\to\:0}(\frac{(0)}{x})
(dy)/(dx)+5y=6	\frac{dy}{dx}+5y=6
integral of 1/((4-x^2)^{3/2)}	\int\:\frac{1}{(4-x^{2})^{\frac{3}{2}}}dx
derivative of-x^3+5ax^2-3a^2x-b	\frac{d}{dx}(-x^{3}+5ax^{2}-3a^{2}x-b)
derivative of e^tcos(3t)	derivative\:e^{t}\cos(3t)
(\partial)/(\partial y)(x/(1+y))	\frac{\partial\:}{\partial\:y}(\frac{x}{1+y})
y^{''}-10y^'+2y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+2y=0
(\partial)/(\partial z)(x/(y+z))	\frac{\partial\:}{\partial\:z}(\frac{x}{y+z})
laplacetransform 4sin(pit)	laplacetransform\:4\sin(πt)
integral of x^3-3x^{-4}+5	\int\:x^{3}-3x^{-4}+5dx
derivative of xx	\frac{d}{dx}(xx)
integral from-1 to 1 of 6-6x^2	\int\:_{-1}^{1}6-6x^{2}dx
(dy)/(dx)=sqrt(10y)e^{x+6}	\frac{dy}{dx}=\sqrt{10y}e^{x+6}
derivative of (e^x/(5-x))	\frac{d}{dx}(\frac{e^{x}}{5-x})
derivative of f(x)=ln(ln(x^3e^{-3x}))	derivative\:f(x)=\ln(\ln(x^{3}e^{-3x}))
(\partial)/(\partial y)(x^2y+y^2z+z^2x)	\frac{\partial\:}{\partial\:y}(x^{2}y+y^{2}z+z^{2}x)
(d^2)/(dx^2)((3x+5)/(2x-1))	\frac{d^{2}}{dx^{2}}(\frac{3x+5}{2x-1})
y^'+xy=xy^{-2}	y^{\prime\:}+xy=xy^{-2}
derivative of 12x-3x^2	\frac{d}{dx}(12x-3x^{2})
maclaurin 1/(1+3x)	maclaurin\:\frac{1}{1+3x}
derivative of sqrt(e^{2x)-1}	\frac{d}{dx}(\sqrt{e^{2x}-1})
derivative of sqrt(ln(x))	derivative\:\sqrt{\ln(x)}
2yy^'+6=y^2+6x	2yy^{\prime\:}+6=y^{2}+6x
integral from 3 to 4 of (5-x^2)-(17-7x)	\int\:_{3}^{4}(5-x^{2})-(17-7x)dx
(\partial)/(\partial x)(x^2tan(xy))	\frac{\partial\:}{\partial\:x}(x^{2}\tan(xy))
(dy)/(dt)=y+t	\frac{dy}{dt}=y+t
d/(dy)(2y^2+3x)	\frac{d}{dy}(2y^{2}+3x)
(\partial)/(\partial x)((53)/(5+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{53}{5+x^{2}+y^{2}})
limit as x approaches 1 of sin(2x)	\lim\:_{x\to\:1}(\sin(2x))
derivative of 5sin(pix)	\frac{d}{dx}(5\sin(πx))
derivative of (x^3/3-4x+1)	\frac{d}{dx}(\frac{x^{3}}{3}-4x+1)
y^{''}-y^'+1/4 y=3+e^{x/2}	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=3+e^{\frac{x}{2}}
derivative of sqrt(4x^3+2)	\frac{d}{dx}(\sqrt{4x^{3}+2})
integral of 2e^{2x}sec^3(e^{2x})	\int\:2e^{2x}\sec^{3}(e^{2x})dx
limit as x approaches 1+of sqrt((x-1)/(x-3))	\lim\:_{x\to\:1+}(\sqrt{\frac{x-1}{x-3}})
integral from 0 to 1 of sqrt(1+36x)	\int\:_{0}^{1}\sqrt{1+36x}dx
integral of cos^3(2θ)sin(2θ)	\int\:\cos^{3}(2θ)\sin(2θ)dθ
integral of 5e^xcos^2(x)	\int\:5e^{x}\cos^{2}(x)dx
integral of y^2(3-y^3)^{2/3}	\int\:y^{2}(3-y^{3})^{\frac{2}{3}}dy
integral of x*sqrt(x^2+1)	\int\:x\cdot\:\sqrt{x^{2}+1}dx
integral of ((x^2))/((4-x^2)^{3/2)}	\int\:\frac{(x^{2})}{(4-x^{2})^{\frac{3}{2}}}dx
limit as x approaches infinity of-(e^x)	\lim\:_{x\to\:\infty\:}(-(e^{x}))
integral of 7/(x(x^4+1))	\int\:\frac{7}{x(x^{4}+1)}dx
y^{''}+10y^'+25y=0,y(0)=-3,y^'(0)=14	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=0,y(0)=-3,y^{\prime\:}(0)=14
tangent of f(x)= 4/(sqrt(x)),\at x= 1/16	tangent\:f(x)=\frac{4}{\sqrt{x}},\at\:x=\frac{1}{16}
integral of (3sqrt(y)-2y-3)	\int\:(3\sqrt{y}-2y-3)dy
derivative of (8x-7^{-5})	\frac{d}{dx}((8x-7)^{-5})
limit as x approaches 0 of sqrt(1+x)-1	\lim\:_{x\to\:0}(\sqrt{1+x}-1)
limit as y approaches 0 of (sin(5y))/(7y)	\lim\:_{y\to\:0}(\frac{\sin(5y)}{7y})
integral of xlog_{e}(x)	\int\:x\log_{e}(x)dx
limit as x approaches 0 of sin^x(x)	\lim\:_{x\to\:0}(\sin^{x}(x))
derivative of cos(x^2-2x)	\frac{d}{dx}(\cos(x^{2}-2x))
derivative of y= 2/(e^x+e^{-x)}	derivative\:y=\frac{2}{e^{x}+e^{-x}}
integral of zcos(z)	\int\:z\cos(z)dz
9y^{''}+10y=0,y(pi)=1	9y^{\prime\:\prime\:}+10y=0,y(π)=1
derivative of 9x^{7/5}-5x^2+10^4	\frac{d}{dx}(9x^{\frac{7}{5}}-5x^{2}+10^{4})
limit as x approaches 0+of-x+7	\lim\:_{x\to\:0+}(-x+7)
(d^2y)/(dx^2)=e^{5x^2}	\frac{d^{2}y}{dx^{2}}=e^{5x^{2}}
d/(dt)((tan^2(3t))/(t^2+sec^2(t)+1))	\frac{d}{dt}(\frac{\tan^{2}(3t)}{t^{2}+\sec^{2}(t)+1})
tangent of f(x)=4-x^2-ln(1/2 x+1)(0.4)	tangent\:f(x)=4-x^{2}-\ln(\frac{1}{2}x+1)(0.4)
integral of e^{-θ}cos(3θ)	\int\:e^{-θ}\cos(3θ)dθ
integral of x/(sqrt(x-4))	\int\:\frac{x}{\sqrt{x-4}}dx
(\partial)/(\partial x)(r^2)	\frac{\partial\:}{\partial\:x}(r^{2})
integral of e^{-st}*e^{at}	\int\:e^{-st}\cdot\:e^{at}dt
tangent of f(x)= 2/(3x+5),(-1,-1)	tangent\:f(x)=\frac{2}{3x+5},(-1,-1)
tangent of f(x)=x^2-2x,\at x=-1	tangent\:f(x)=x^{2}-2x,\at\:x=-1
y^'+5y=2sin(e^{5x})	y^{\prime\:}+5y=2\sin(e^{5x})
integral from 2 to 6 of t^3ln(5x)	\int\:_{2}^{6}t^{3}\ln(5x)dx
inverse oflaplace 1/((s^2-1))	inverselaplace\:\frac{1}{(s^{2}-1)}
(\partial)/(\partial x)(7+xln(xy-5))	\frac{\partial\:}{\partial\:x}(7+x\ln(xy-5))
d/(dy)(2y)	\frac{d}{dy}(2y)
integral from 0 to x of ylog_{10}(y)	\int\:_{0}^{x}y\log_{10}(y)dy
sum from n=3 to infinity of (4^n)/(7^n)	\sum\:_{n=3}^{\infty\:}\frac{4^{n}}{7^{n}}
integral of x^4y^3	\int\:x^{4}y^{3}dy
area x=9y^2,x=2+7y^2	area\:x=9y^{2},x=2+7y^{2}
inverse oflaplace x^{-1/2}	inverselaplace\:x^{-\frac{1}{2}}
integral from-1 to 1 of (-x^2+1)^2	\int\:_{-1}^{1}(-x^{2}+1)^{2}dx
integral of-32x+38	\int\:-32x+38dx
integral from-1/2 to 1/2 of 2arccos(2x)	\int\:_{-\frac{1}{2}}^{\frac{1}{2}}2\arccos(2x)dx
(d^2)/(dx^2)(x^3-3/x)	\frac{d^{2}}{dx^{2}}(x^{3}-\frac{3}{x})
derivative of arccot(x^3)	\frac{d}{dx}(\arccot(x^{3}))
integral of 8x+1-9e^x	\int\:8x+1-9e^{x}dx
limit as x approaches 0 of (x+1) 3/x	\lim\:_{x\to\:0}((x+1)\frac{3}{x})
tangent of f(x)=x^3-3x+2,(4,54)	tangent\:f(x)=x^{3}-3x+2,(4,54)
integral from 0 to 2 of (15sqrt(4x+1))	\int\:_{0}^{2}(15\sqrt{4x+1})dx
limit as x approaches 2 of (x-3)/(x+4)	\lim\:_{x\to\:2}(\frac{x-3}{x+4})
integral of xcos(7pi)x^2	\int\:x\cos(7π)x^{2}dx
derivative of f(r)= 3/(r^3)	derivative\:f(r)=\frac{3}{r^{3}}
sum from n=1 to infinity of (x^n)/(n3^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{n3^{n}}

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