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Popular Calculus Problems

integral of 1/(3xsqrt(9x^2-12))	\int\:\frac{1}{3x\sqrt{9x^{2}-12}}dx
derivative of e^{-1}	derivative\:e^{-1}
integral from 0 to 2 of e^{-x}+e	\int\:_{0}^{2}e^{-x}+edx
integral of te^{-6t}	\int\:te^{-6t}dt
derivative of (2x^2+6x+6/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+6x+6}{\sqrt{x}})
sum from n=1 to infinity of 4(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}4(0.8)^{n-1}
dx+e^{3x}dy=0	dx+e^{3x}dy=0
(d^2)/(dx^2)(-5/x)	\frac{d^{2}}{dx^{2}}(-\frac{5}{x})
derivative of (-10/(x^3))	\frac{d}{dx}(\frac{-10}{x^{3}})
e^xydy-(e^{-y}+e^{2x-y})dx=0	e^{x}ydy-(e^{-y}+e^{2x-y})dx=0
derivative of log_{e}(x^2+1)	\frac{d}{dx}(\log_{e}(x^{2}+1))
integral of (e^{3x})/(sqrt(1-e^{6x))}	\int\:\frac{e^{3x}}{\sqrt{1-e^{6x}}}dx
limit as x approaches infinity of (5-2x^{3/2})/(3x-4)	\lim\:_{x\to\:\infty\:}(\frac{5-2x^{\frac{3}{2}}}{3x-4})
integral of (1-x)(2+x^2)	\int\:(1-x)(2+x^{2})dx
derivative of arctan(7/(x^2))	derivative\:\arctan(\frac{7}{x^{2}})
derivative of (3sqrt(x)+4)x^2	derivative\:(3\sqrt{x}+4)x^{2}
integral of 7(sec(x))^2-4sin(x)	\int\:7(\sec(x))^{2}-4\sin(x)dx
integral of sqrt(x^2-3/4)	\int\:\sqrt{x^{2}-\frac{3}{4}}dx
derivative of sin(pi)	\frac{d}{dx}(\sin(π))
derivative of (x^3+2e^x)	\frac{d}{dx}((x^{3}+2)e^{x})
y^{''}-2y=5	y^{\prime\:\prime\:}-2y=5
integral of ((3inx-5)^4)/x	\int\:\frac{(3inx-5)^{4}}{x}dx
(dy)/(dx)=5y^2-y/x	\frac{dy}{dx}=5y^{2}-\frac{y}{x}
derivative of y=sqrt(x^2-1)arcsec(x)	derivative\:y=\sqrt{x^{2}-1}\arcsec(x)
laplacetransform 6(t)e^{-2t}	laplacetransform\:6(t)e^{-2t}
(\partial)/(\partial x)((1+2xy^2)^3)	\frac{\partial\:}{\partial\:x}((1+2xy^{2})^{3})
derivative of y= t/((t-5)^2)	derivative\:y=\frac{t}{(t-5)^{2}}
integral of 5cos^3(6x)	\int\:5\cos^{3}(6x)dx
(\partial)/(\partial x)(3x^3+x^2y-3y^3)	\frac{\partial\:}{\partial\:x}(3x^{3}+x^{2}y-3y^{3})
roots ax^2	roots\:ax^{2}
integral of 13x^2sin(pix)	\int\:13x^{2}\sin(πx)dx
tangent of y=10sqrt(x)-x+3,(100,3)	tangent\:y=10\sqrt{x}-x+3,(100,3)
integral from 0 to 10 of 2piy(100-y^2)	\int\:_{0}^{10}2πy(100-y^{2})dy
integral of x^20.4^{-x}x	\int\:x^{2}0.4^{-x}xdx
slope ofintercept (4,5),(1,-3)	slopeintercept\:(4,5),(1,-3)
t^2y^{''}-11ty^'+35y=0	t^{2}y^{\prime\:\prime\:}-11ty^{\prime\:}+35y=0
integral of (x^4+8)/(x^3)	\int\:\frac{x^{4}+8}{x^{3}}dx
y^{''}+y=2csc^2(t)	y^{\prime\:\prime\:}+y=2\csc^{2}(t)
integral from 0 to c of 4e^{2x}	\int\:_{0}^{c}4e^{2x}dx
integral from 0 to 1 of (e^x-xe^{x^2})	\int\:_{0}^{1}(e^{x}-xe^{x^{2}})dx
integral of v/(1-v)	\int\:\frac{v}{1-v}dv
integral of-x+3(cos((npix)/8))	\int\:-x+3(\cos(\frac{n\cdot\:π\cdot\:x}{8}))dx
derivative of 1/(sqrt(xy))	\frac{d}{dx}(\frac{1}{\sqrt{xy}})
(x^2-xy)(dy)/(dx)+y^2=0	(x^{2}-xy)\frac{dy}{dx}+y^{2}=0
y=sqrt(t)	y=\sqrt{t}
integral of (2x-1)/(x^2)	\int\:\frac{2x-1}{x^{2}}dx
derivative of 3x^3-x^2+9x-9	derivative\:3x^{3}-x^{2}+9x-9
inverse oflaplace (s-2)/(s^2-s-6)	inverselaplace\:\frac{s-2}{s^{2}-s-6}
derivative of (arcsin(3x)/x)	\frac{d}{dx}(\frac{\arcsin(3x)}{x})
tangent of f(x)=3-4x^2,\at x=-2	tangent\:f(x)=3-4x^{2},\at\:x=-2
tangent of y=sqrt(3x),(3,3)	tangent\:y=\sqrt{3x},(3,3)
integral of e^{6-5t}	\int\:e^{6-5t}dt
integral of xsin(3t-3x)	\int\:x\sin(3t-3x)dx
(\partial)/(\partial y)(sqrt(3x+2y))	\frac{\partial\:}{\partial\:y}(\sqrt{3x+2y})
derivative of (8+x{f}(x)/(sqrt(x)))	\frac{d}{dx}(\frac{8+x{f}(x)}{\sqrt{x}})
integral of sin(x) 1/x	\int\:\sin(x)\frac{1}{x}dx
(\partial)/(\partial y)(sqrt(2x^2+2y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{2x^{2}+2y^{2}})
(dy)/(dx)=x*e^{-2x},y(0)=3	\frac{dy}{dx}=x\cdot\:e^{-2x},y(0)=3
limit as x approaches 1 of (\sqrt[3]{1-x^2})/(\sqrt[3]{1-x^3)}	\lim\:_{x\to\:1}(\frac{\sqrt[3]{1-x^{2}}}{\sqrt[3]{1-x^{3}}})
integral of sin(nx)	\int\:\sin(nx)dx
integral of 1/((1+2x^2))	\int\:\frac{1}{(1+2x^{2})}dx
limit as x approaches pi/2+of tan(x)	\lim\:_{x\to\:\frac{π}{2}+}(\tan(x))
xy^'=xe^x-2y	xy^{\prime\:}=xe^{x}-2y
limit as x approaches-6 of x^2	\lim\:_{x\to\:-6}(x^{2})
tangent of 4+2x+10xe^x	tangent\:4+2x+10xe^{x}
derivative of f(x)=(3-5xe^x)(3x+2)	derivative\:f(x)=(3-5xe^{x})(3x+2)
integral from 1 to 5 of (x^2-x+1)	\int\:_{1}^{5}(x^{2}-x+1)dx
derivative of-sin(4x)	\frac{d}{dx}(-\sin(4x))
derivative of y=e^{x^4}	derivative\:y=e^{x^{4}}
(dy)/(dx)=(1+e^{2x})	\frac{dy}{dx}=(1+e^{2x})
derivative of (x^2/(x-9))	\frac{d}{dx}(\frac{x^{2}}{x-9})
slope of (-8,9),(-2,-3)	slope\:(-8,9),(-2,-3)
xy+y^'=100x	xy+y^{\prime\:}=100x
integral from-3 to 1 of 2x+2	\int\:_{-3}^{1}2x+2dx
tangent of f(x)=x^3-3x^2+1	tangent\:f(x)=x^{3}-3x^{2}+1
integral of (1+x^5)^35x^4	\int\:(1+x^{5})^{3}5x^{4}dx
integral of (x^5)/(sqrt(x^2+5))	\int\:\frac{x^{5}}{\sqrt{x^{2}+5}}dx
(\partial)/(\partial t)(st)	\frac{\partial\:}{\partial\:t}(st)
integral of 3xsqrt(5+x^2)	\int\:3x\sqrt{5+x^{2}}dx
integral of cos(2y)	\int\:\cos(2y)dy
integral of 1/(xsqrt(x))	\int\:\frac{1}{x\sqrt{x}}dx
limit as x approaches 1 of 2x^2-4x+2	\lim\:_{x\to\:1}(2x^{2}-4x+2)
(\partial)/(\partial y)((3y)/(x^5))	\frac{\partial\:}{\partial\:y}(\frac{3y}{x^{5}})
y^{''}-3y^'+4y=xe^x	y^{\prime\:\prime\:}-3y^{\prime\:}+4y=xe^{x}
derivative of 1(-5x+3(-3x+2))	\frac{d}{dx}(1(-5x+3)(-3x+2))
integral of ((e^x))/(e^x+1)	\int\:\frac{(e^{x})}{e^{x}+1}dx
(\partial)/(\partial x)(x^2-2xy+y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-2xy+y^{2})
integral of 1/(ln(x))	\int\:\frac{1}{\ln(x)}dx
integral of (y+1)/(y-1)	\int\:\frac{y+1}{y-1}dy
y^{''}-5y^'=x-2	y^{\prime\:\prime\:}-5y^{\prime\:}=x-2
derivative of 3x^2cos(x)cot(x)	derivative\:3x^{2}\cos(x)\cot(x)
derivative of e^xsin(2x)	derivative\:e^{x}\sin(2x)
derivative of ln(x/k)	\frac{d}{dx}(\ln(\frac{x}{k}))
integral from-a to a of 1/((s-x)^2)	\int\:_{-a}^{a}\frac{1}{(s-x)^{2}}dx
derivative of (x^2-4/(x^2-2x))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}-2x})
integral of 2/(x^{2/3)}	\int\:\frac{2}{x^{\frac{2}{3}}}dx
2y*(dy)/(dx)=x(y^2+1)	2y\cdot\:\frac{dy}{dx}=x(y^{2}+1)
derivative of in(x^2-5)	\frac{d}{dx}(in(x^{2}-5))
y^'=1-e^{x-y+8}	y^{\prime\:}=1-e^{x-y+8}
inverse oflaplace 5/(8s)	inverselaplace\:\frac{5}{8s}

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