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Popular Calculus Problems

integral of (1/x-2/(x^2)+5/(x^3))	\int\:(\frac{1}{x}-\frac{2}{x^{2}}+\frac{5}{x^{3}})dx
laplacetransform-y	laplacetransform\:-y
limit as x approaches 0 of 4x-ln(4x+1)	\lim\:_{x\to\:0}(4x-\ln(4x+1))
limit as x approaches 0 of (12)/(x^2)	\lim\:_{x\to\:0}(\frac{12}{x^{2}})
y^{''}+y^'+a^2y=0	y^{\prime\:\prime\:}+y^{\prime\:}+a^{2}y=0
integral of (1+6x)/((4x-3)(2x+5))	\int\:\frac{1+6x}{(4x-3)(2x+5)}dx
5xy^'=2xe^x-5y+6x^2	5xy^{\prime\:}=2xe^{x}-5y+6x^{2}
limit as x approaches 0+of (7x)/x	\lim\:_{x\to\:0+}(\frac{7x}{x})
6y^{''}+8y^'+9y=0	6y^{\prime\:\prime\:}+8y^{\prime\:}+9y=0
y^{''}+6y^'+8y=3e^{-2x}+2x	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=3e^{-2x}+2x
(\partial)/(\partial x)(2sqrt(x))	\frac{\partial\:}{\partial\:x}(2\sqrt{x})
integral of 2cos(2θ)	\int\:2\cos(2θ)dθ
slope ofintercept (2,59),(4,91)	slopeintercept\:(2,59),(4,91)
f(t)=sin(3t)	f(t)=\sin(3t)
(\partial)/(\partial x)(e^xcos(y)+x)	\frac{\partial\:}{\partial\:x}(e^{x}\cos(y)+x)
(\partial)/(\partial x)(8y-x^4sin(xy))	\frac{\partial\:}{\partial\:x}(8y-x^{4}\sin(xy))
derivative of-6x+1	\frac{d}{dx}(-6x+1)
(\partial)/(\partial x)(zsin(xy^2+2z))	\frac{\partial\:}{\partial\:x}(z\sin(xy^{2}+2z))
(\partial)/(\partial x)(xy+z^3x-2yz)	\frac{\partial\:}{\partial\:x}(xy+z^{3}x-2yz)
(\partial)/(\partial x)(sin(x-y^2))	\frac{\partial\:}{\partial\:x}(\sin(x-y^{2}))
integral from-1 to 2 of (x+2-x^2)^2	\int\:_{-1}^{2}(x+2-x^{2})^{2}dx
limit as t approaches 1 of f(t)	\lim\:_{t\to\:1}(f(t))
y^{''}+16y=5sec(4t)	y^{\prime\:\prime\:}+16y=5\sec(4t)
integral of 1/((s^2-2s+1)^2)	\int\:\frac{1}{(s^{2}-2s+1)^{2}}ds
integral from 0 to 7 of (e^t+e^{-t})	\int\:_{0}^{7}(e^{t}+e^{-t})dt
limit as x approaches 0+of (1+x)^{1/x}	\lim\:_{x\to\:0+}((1+x)^{\frac{1}{x}})
tangent of y=3e^{-x},(0,3)	tangent\:y=3e^{-x},(0,3)
(dy)/(dx)+(3xy)/(x^2+1)=(6x)/(x^2+1)	\frac{dy}{dx}+\frac{3xy}{x^{2}+1}=\frac{6x}{x^{2}+1}
integral of 1/(4+8x)	\int\:\frac{1}{4+8x}dx
integral of 7x^{2/5}+3x^{-4/5}	\int\:7x^{\frac{2}{5}}+3x^{-\frac{4}{5}}dx
y^{'''}-5y^{''}+3y^'+9y=0	y^{\prime\:\prime\:\prime\:}-5y^{\prime\:\prime\:}+3y^{\prime\:}+9y=0
limit as x approaches-10 of-15	\lim\:_{x\to\:-10}(-15)
derivative of x,pix	\frac{d}{dx}(x,πx)
tangent of (10)/(1+e^{-x)}	tangent\:\frac{10}{1+e^{-x}}
integral of 1/(x^2(2x-1))	\int\:\frac{1}{x^{2}(2x-1)}dx
derivative of x^3+x-1	\frac{d}{dx}(x^{3}+x-1)
derivative of 2e^{(x-5)}	derivative\:2e^{(x-5)}
derivative of (x-4)/(x+4)	derivative\:\frac{x-4}{x+4}
(dy)/(dx)=2sqrt(y)	\frac{dy}{dx}=2\sqrt{y}
limit as x approaches 0 of sin((40pi)/x)	\lim\:_{x\to\:0}(\sin(\frac{40π}{x}))
inverse oflaplace 1/((s+2)^4)	inverselaplace\:\frac{1}{(s+2)^{4}}
derivative of ((4x^2)/(2-x))^3	derivative\:(\frac{4x^{2}}{2-x})^{3}
integral of-2ln(x^2-1)	\int\:-2\ln(x^{2}-1)dx
derivative of f(x)=11x-1	derivative\:f(x)=11x-1
limit as x approaches 4 of (3x-3)^{5/2}	\lim\:_{x\to\:4}((3x-3)^{\frac{5}{2}})
integral of ((14x^3+2x+1))/(x^3)	\int\:\frac{(14x^{3}+2x+1)}{x^{3}}dx
derivative of sin(x^2-2x+6)	\frac{d}{dx}(\sin(x^{2}-2x+6))
area y^2=x+1,x=1	area\:y^{2}=x+1,x=1
integral of sin^{10}(x)	\int\:\sin^{10}(x)dx
tangent of f(x)= 4/(x^2),(1,4)	tangent\:f(x)=\frac{4}{x^{2}},(1,4)
derivative of f(x)=(3-e^{-4x})^4	derivative\:f(x)=(3-e^{-4x})^{4}
derivative of sqrt(2+2cos(x))	\frac{d}{dx}(\sqrt{2+2\cos(x)})
area 29-11x,1-x^2	area\:29-11x,1-x^{2}
derivative of \sqrt[7]{x}-8/x	\frac{d}{dx}(\sqrt[7]{x}-\frac{8}{x})
(d^2y)/(dx^2)+5(dy)/(dx)+6y=2e^x	\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}+6y=2e^{x}
derivative of y=x^{3cos(x)}	derivative\:y=x^{3\cos(x)}
integral of sqrt(x^5)	\int\:\sqrt{x^{5}}dx
integral of sec(t)(sec(t)-tan(t))	\int\:\sec(t)(\sec(t)-\tan(t))dt
derivative of 1/({f(x)(x)^{-1}(x)})	\frac{d}{dx}(\frac{1}{{f}(x)(x)^{-1}(x)})
ds=2sqrt(s)dt	ds=2\sqrt{s}dt
sum from n=0 to infinity of 5(-1/3)^n	\sum\:_{n=0}^{\infty\:}5(-\frac{1}{3})^{n}
limit as x approaches 4 of ((x^2-16))/(2-sqrt(x))	\lim\:_{x\to\:4}(\frac{(x^{2}-16)}{2-\sqrt{x}})
derivative of ln(2e^{-x}sin(x))	\frac{d}{dx}(\ln(2e^{-x}\sin(x)))
integral of sqrt(1+(tan(x))^2)	\int\:\sqrt{1+(\tan(x))^{2}}dx
derivative of g(x)=sqrt(6-x)	derivative\:g(x)=\sqrt{6-x}
taylor 1/(1-x),0,1	taylor\:\frac{1}{1-x},0,1
integral of 3x^5	\int\:3x^{5}dx
sum from n=9 to infinity of e^{3-4n}	\sum\:_{n=9}^{\infty\:}e^{3-4n}
derivative of y=cos^4(x)-sin^4(x)	derivative\:y=\cos^{4}(x)-\sin^{4}(x)
integral of sin^3(x)cos(x	\int\:\sin^{3}(x)\cos(d)xdx
taylor x^2-2x+4	taylor\:x^{2}-2x+4
integral of (7x^3+4x^2)	\int\:(7x^{3}+4x^{2})dx
derivative of f(x)=4x-x^2	derivative\:f(x)=4x-x^{2}
integral of 36sin^2(x)	\int\:36\sin^{2}(x)dx
derivative of (1+sqrt(t))(4t^2-9)	derivative\:(1+\sqrt{t})(4t^{2}-9)
derivative of (1-cos(x))/(1+x-e^x)	derivative\:\frac{1-\cos(x)}{1+x-e^{x}}
derivative of 5x+5	\frac{d}{dx}(5x+5)
derivative of y(θ)=arctan(cos(θ))	derivative\:y(θ)=\arctan(\cos(θ))
integral of x(2-x)^2	\int\:x(2-x)^{2}dx
integral from 0 to 5 of xsqrt(1+x)	\int\:_{0}^{5}x\sqrt{1+x}dx
derivative of e^{x^3+2x}	derivative\:e^{x^{3}+2x}
integral of (7+x+x^2)/(sqrt(x))	\int\:\frac{7+x+x^{2}}{\sqrt{x}}dx
derivative of f(x)=sqrt(8x^2-x)	derivative\:f(x)=\sqrt{8x^{2}-x}
derivative of sin(pi/x)	\frac{d}{dx}(\sin(\frac{π}{x}))
(\partial)/(\partial x)(ln(x^3+y^7))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}+y^{7}))
derivative of sin^{-5}(x-cos^3(x))	\frac{d}{dx}(\sin^{-5}(x)-\cos^{3}(x))
integral of ((x+1))/(sqrt(x))	\int\:\frac{(x+1)}{\sqrt{x}}dx
(csc^2(x))^'	(\csc^{2}(x))^{\prime\:}
integral of x/(sqrt(25-x^2))	\int\:\frac{x}{\sqrt{25-x^{2}}}dx
implicit (dy)/(dx),y^3=x^2	implicit\:\frac{dy}{dx},y^{3}=x^{2}
derivative of 2x^3+3x^2-12x+5	\frac{d}{dx}(2x^{3}+3x^{2}-12x+5)
derivative of tan(3x+1)	\frac{d}{dx}(\tan(3x+1))
integral of 19sin^2(x)cos^2(x)	\int\:19\sin^{2}(x)\cos^{2}(x)dx
derivative of y=(x+1)/(2x-1)	derivative\:y=\frac{x+1}{2x-1}
y^'-y=e^{2x}	y^{\prime\:}-y=e^{2x}
integral of 12cos(4x)	\int\:12\cos(4x)dx
derivative of f(x)=5x+1	derivative\:f(x)=5x+1
limit as x approaches 0-of (x^2)/6-5/x	\lim\:_{x\to\:0-}(\frac{x^{2}}{6}-\frac{5}{x})
derivative of 1/3 x^3-x	\frac{d}{dx}(\frac{1}{3}x^{3}-x)
limit as x approaches 0 of x^3-4x^2	\lim\:_{x\to\:0}(x^{3}-4x^{2})

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