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Popular Calculus Problems

integral from 3 to 6 of (x^2)	\int\:_{3}^{6}(x^{2})dx
integral from-4 to-6 of (-2)^{-3}	\int\:_{-4}^{-6}(-2)^{-3}dx
integral from 0 to pi of sin(2x)	\int\:_{0}^{π}\sin(2x)dx
integral of 1/((x^2+7))	\int\:\frac{1}{(x^{2}+7)}dx
slope of y=sqrt(1-4x),\at x=-1	slope\:y=\sqrt{1-4x},\at\:x=-1
limit as x approaches 9-of x/(x-9)	\lim\:_{x\to\:9-}(\frac{x}{x-9})
integral of-ln(cos(x))	\int\:-\ln(\cos(x))dx
limit as x approaches 0 of 2x-xln(x)	\lim\:_{x\to\:0}(2x-x\ln(x))
derivative of 3x^2+2x+5	\frac{d}{dx}(3x^{2}+2x+5)
limit as x approaches 0 of (7x)^{3x}	\lim\:_{x\to\:0}((7x)^{3x})
integral of-cos(x)+sin(x)+3	\int\:-\cos(x)+\sin(x)+3dx
integral of (cos(x))/(sin^6(x))	\int\:\frac{\cos(x)}{\sin^{6}(x)}dx
(dy)/(dx)= x/(18y)	\frac{dy}{dx}=\frac{x}{18y}
(2x+t)(dx)/(dt)+(x-2t)=0	(2x+t)\frac{dx}{dt}+(x-2t)=0
integral of-2csc^2(x)	\int\:-2\csc^{2}(x)dx
limit as x approaches 0 of x^3*csc^2(x)	\lim\:_{x\to\:0}(x^{3}\cdot\:\csc^{2}(x))
f(x)=sin^5(2x)cos^3(2x)	f(x)=\sin^{5}(2x)\cos^{3}(2x)
(x^2-1)y^'=2y	(x^{2}-1)y^{\prime\:}=2y
tangent of y=(x^2+1)/(3x+1),\at x=0	tangent\:y=\frac{x^{2}+1}{3x+1},\at\:x=0
(\partial)/(\partial y)(Ax+By^2+Cx^2y)	\frac{\partial\:}{\partial\:y}(Ax+By^{2}+Cx^{2}y)
ydx+(y-x)dy=0	ydx+(y-x)dy=0
slope of (0.3)(2.5)	slope\:(0.3)(2.5)
integral of x^5*ln(3x^2)	\int\:x^{5}\cdot\:\ln(3x^{2})dx
integral of 1/(x+5)	\int\:\frac{1}{x+5}dx
integral of 1/(t^2)sin(2/1+3)	\int\:\frac{1}{t^{2}}\sin(\frac{2}{1}+3)dt
derivative of sec(xanx)	\frac{d}{dx}(\sec(x)anx)
derivative of (x^2+1^{3/2})	\frac{d}{dx}((x^{2}+1)^{\frac{3}{2}})
(\partial)/(\partial y)(x^2+sin(xy))	\frac{\partial\:}{\partial\:y}(x^{2}+\sin(xy))
integral from 0 to 1 of cos(x)	\int\:_{0}^{1}\cos(x)dx
4y^{''}-y^'+2y=0,y(0)=2,y^'(0)=0	4y^{\prime\:\prime\:}-y^{\prime\:}+2y=0,y(0)=2,y^{\prime\:}(0)=0
limit as x approaches 3 of (3-x)/(\|3-x\|)	\lim\:_{x\to\:3}(\frac{3-x}{\left\|3-x\right\|})
(\partial)/(\partial x)(3xe^{3xy})	\frac{\partial\:}{\partial\:x}(3xe^{3xy})
limit as x approaches-infinity of 0^x	\lim\:_{x\to\:-\infty\:}(0^{x})
limit as x approaches 0+of ln(5)sin(x)	\lim\:_{x\to\:0+}(\ln(5)\sin(x))
integral from 4 to 16 of 1/(6-sqrt(x))	\int\:_{4}^{16}\frac{1}{6-\sqrt{x}}dx
implicit (dy)/(dx),xy=8	implicit\:\frac{dy}{dx},xy=8
integral of-(e^{-st})/s	\int\:-\frac{e^{-st}}{s}dt
inverse oflaplace ((s+4))/((s+1)^2)	inverselaplace\:\frac{(s+4)}{(s+1)^{2}}
tangent of y=(1+3x)^9,(0,1)	tangent\:y=(1+3x)^{9},(0,1)
tangent of 6/(x-1)	tangent\:\frac{6}{x-1}
derivative of 2(x^3-x^4)	\frac{d}{dx}(2(x^{3}-x)^{4})
derivative of x^2-xy+y^2	\frac{d}{dx}(x^{2}-xy+y^{2})
integral from 0 to 1 of (63)/(4y-1)	\int\:_{0}^{1}\frac{63}{4y-1}dy
derivative of e^x(3x^2-6x+6)	derivative\:e^{x}(3x^{2}-6x+6)
limit as x approaches 0-of 7-2sqrt(x)	\lim\:_{x\to\:0-}(7-2\sqrt{x})
integral of 3x^3-5x^2+3x+4	\int\:3x^{3}-5x^{2}+3x+4dx
derivative of (x+1)^{x+1}	derivative\:(x+1)^{x+1}
f(θ)=e^θ	f(θ)=e^{θ}
derivative of cos(e^{4x})	\frac{d}{dx}(\cos(e^{4x}))
derivative of f(x)=(7x^2-6x+1)/(3x+2)	derivative\:f(x)=\frac{7x^{2}-6x+1}{3x+2}
(d^2)/(dx^2)(3+5x+2x^2+0.4x^3)	\frac{d^{2}}{dx^{2}}(3+5x+2x^{2}+0.4x^{3})
y^{''}+9y=2sin(3x)	y^{\prime\:\prime\:}+9y=2\sin(3x)
y^'=4sqrt(x)y	y^{\prime\:}=4\sqrt{x}y
integral of (x^2-x+1)/(sqrt((x^2+1)^3))	\int\:\frac{x^{2}-x+1}{\sqrt{(x^{2}+1)^{3}}}dx
derivative of 3e^x+8/(\sqrt[3]{x)}	derivative\:3e^{x}+\frac{8}{\sqrt[3]{x}}
integral of 6/(sqrt(1-x^2))	\int\:\frac{6}{\sqrt{1-x^{2}}}dx
derivative of ln(sqrt(pi))	\frac{d}{dx}(\ln(\sqrt{π}))
sum from n=1 to infinity of n^{-1/3}	\sum\:_{n=1}^{\infty\:}n^{-\frac{1}{3}}
integral of (x^3-x^2)/(x^2)	\int\:\frac{x^{3}-x^{2}}{x^{2}}dx
derivative of cos(2x^3-x)	\frac{d}{dx}(\cos(2x^{3}-x))
integral of e^{sqrt(4x)}	\int\:e^{\sqrt{4x}}dx
integral of (csc(5x))^3	\int\:(\csc(5x))^{3}dx
derivative of f(x)=ln(x+2)	derivative\:f(x)=\ln(x+2)
derivative of sin((5x-3x^3/(x+1)))	\frac{d}{dx}(\sin(\frac{5x-3x^{3}}{x+1}))
taylor x^n	taylor\:x^{n}
integral of (3x^2+x+1)/(x^2-2x+5)	\int\:\frac{3x^{2}+x+1}{x^{2}-2x+5}dx
derivative of arctan(2/x)	derivative\:\arctan(\frac{2}{x})
x^2y^{''}+y^'=0	x^{2}y^{\prime\:\prime\:}+y^{\prime\:}=0
integral from 0 to 1 of x^6(1+2x^7)^5	\int\:_{0}^{1}x^{6}(1+2x^{7})^{5}dx
derivative of f(x)=x^4sqrt(sec(5x))	derivative\:f(x)=x^{4}\sqrt{\sec(5x)}
(\partial)/(\partial x)(sin(x^2)y)	\frac{\partial\:}{\partial\:x}(\sin(x^{2})y)
integral from 2 to infinity of e^{-5x}	\int\:_{2}^{\infty\:}e^{-5x}dx
integral of 7ln(x^2-x+2)	\int\:7\ln(x^{2}-x+2)dx
derivative of 2x^2+cos^2(x)	\frac{d}{dx}(2x^{2}+\cos^{2}(x))
derivative of cos((3x^2/(x+2)))	\frac{d}{dx}(\cos(\frac{3x^{2}}{x+2}))
limit as x approaches 2 of [7f(x)+g(x)]	\lim\:_{x\to\:2}([7f(x)+g(x)])
implicit (dy)/(dx),xy=56	implicit\:\frac{dy}{dx},xy=56
(\partial)/(\partial x)(sin(pi(x-4y)))	\frac{\partial\:}{\partial\:x}(\sin(π(x-4y)))
integral of (6x^2-4x+3)	\int\:(6x^{2}-4x+3)dx
(\partial)/(\partial x)(ln(x^{10}y))	\frac{\partial\:}{\partial\:x}(\ln(x^{10}y))
derivative of f(x)=x^2-2x+2	derivative\:f(x)=x^{2}-2x+2
derivative of (sqrt(1-x))/2	derivative\:\frac{\sqrt{1-x}}{2}
(xsqrt(1+y^2))dx-x^2dy=0	(x\sqrt{1+y^{2}})dx-x^{2}dy=0
integral of 4/((x^2)(x^2+4))	\int\:\frac{4}{(x^{2})(x^{2}+4)}dx
area 2x^2,8x^2,5-3x	area\:2x^{2},8x^{2},5-3x
(\partial)/(\partial x)(4x^2y+7xy^3)	\frac{\partial\:}{\partial\:x}(4x^{2}y+7xy^{3})
derivative of f(x)=(3x-2)(4x^3-x^2+1)	derivative\:f(x)=(3x-2)(4x^{3}-x^{2}+1)
derivative of 6xe^{x^2}	\frac{d}{dx}(6xe^{x^{2}})
limit as x approaches 2 of x^2-6x+3	\lim\:_{x\to\:2}(x^{2}-6x+3)
derivative of 1/(1+e^{0.5x})	\frac{d}{dx}(\frac{1}{1+e^{0.5x}})
sum from n=1 to infinity of ne^{-6n}	\sum\:_{n=1}^{\infty\:}ne^{-6n}
(d^2)/(dz^2)(z^2e^z)	\frac{d^{2}}{dz^{2}}(z^{2}e^{z})
integral of (sqrt(x^2+1))	\int\:(\sqrt{x^{2}+1})dx
(d^2)/(dx^2)(6x^2+5x)	\frac{d^{2}}{dx^{2}}(6x^{2}+5x)
(t+1)dt-1/(y^2)dy=0	(t+1)dt-\frac{1}{y^{2}}dy=0
integral of (2w-5)/(w^2-3w+9/2)	\int\:\frac{2w-5}{w^{2}-3w+\frac{9}{2}}dx
area 2x+y^2=8,x=y	area\:2x+y^{2}=8,x=y
(\partial)/(\partial x)(6xy-2y^2)	\frac{\partial\:}{\partial\:x}(6xy-2y^{2})
derivative of 4/(7x^2)	\frac{d}{dx}(\frac{4}{7x^{2}})
integral of (x+7)/(x^2+3x+2)	\int\:\frac{x+7}{x^{2}+3x+2}dx

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