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Popular Calculus Problems

laplacetransform te^{-2t}	laplacetransform\:te^{-2t}
(\partial)/(\partial x)(y/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{y}{x+1})
inverse oflaplace s/1	inverselaplace\:\frac{s}{1}
(\partial)/(\partial x)(-x^2y+1/y)	\frac{\partial\:}{\partial\:x}(-x^{2}y+\frac{1}{y})
integral from 1 to 3 of 2^x	\int\:_{1}^{3}2^{x}dx
f(x)=sqrt(x^2+36)	f(x)=\sqrt{x^{2}+36}
integral of 1/(x-70)	\int\:\frac{1}{x-70}dx
integral of (9x^2-8x+4)/(x^3+4x)	\int\:\frac{9x^{2}-8x+4}{x^{3}+4x}dx
(\partial)/(\partial x)(6x^4y-3xy+2y)	\frac{\partial\:}{\partial\:x}(6x^{4}y-3xy+2y)
limit as x approaches 2 of 3-x	\lim\:_{x\to\:2}(3-x)
integral from 0 to pi of 2pisin(x)	\int\:_{0}^{π}2π\sin(x)dx
xy'=2y	xy\prime\:=2y
integral of 1/(sqrt(36-x^2))	\int\:\frac{1}{\sqrt{36-x^{2}}}dx
taylor 1/(1-x^3),0	taylor\:\frac{1}{1-x^{3}},0
integral of ((4x-2))/(x^3-x^2-2x)	\int\:\frac{(4x-2)}{x^{3}-x^{2}-2x}dx
derivative of 5/3 x^3+x^2-1	\frac{d}{dx}(\frac{5}{3}x^{3}+x^{2}-1)
integral of (sin^7(ln(x)))/x	\int\:\frac{\sin^{7}(\ln(x))}{x}dx
1/(x^8)y^'=12+15y	\frac{1}{x^{8}}y^{\prime\:}=12+15y
(\partial)/(\partial x)(x^2y+xy^2)	\frac{\partial\:}{\partial\:x}(x^{2}y+xy^{2})
tangent of y=x^3,\at x=-9	tangent\:y=x^{3},\at\:x=-9
derivative of (1+sin(x))^{-4}	derivative\:(1+\sin(x))^{-4}
integral of (1/x+1/(3-x))	\int\:(\frac{1}{x}+\frac{1}{3-x})dx
limit as x approaches 0 of sin(5x)csc(3x)	\lim\:_{x\to\:0}(\sin(5x)\csc(3x))
laplacetransform 0.02(1+3cos(t))	laplacetransform\:0.02(1+3\cos(t))
(dy)/(dt)=25-10t-2y	\frac{dy}{dt}=25-10t-2y
area 2(x+1),3(x+1),x=3	area\:2(x+1),3(x+1),x=3
integral from-pi/6 to 0 of 6sec^3(x)	\int\:_{-\frac{π}{6}}^{0}6\sec^{3}(x)dx
derivative of-sin(xcos(x))	\frac{d}{dx}(-\sin(x)\cos(x))
derivative of (2x-3/(5x+4))	\frac{d}{dx}(\frac{2x-3}{5x+4})
integral of (x+6)(x-4)	\int\:(x+6)(x-4)dx
integral of 5/(2x-1)	\int\:\frac{5}{2x-1}dx
integral from 5 to 8 of (x-7)^2	\int\:_{5}^{8}(x-7)^{2}dx
(dy)/(dx)= 1/(y^3)	\frac{dy}{dx}=\frac{1}{y^{3}}
limit as x approaches-2+of (x+1)/(x+2)	\lim\:_{x\to\:-2+}(\frac{x+1}{x+2})
integral of 1/(xsqrt(4x^2-16))	\int\:\frac{1}{x\sqrt{4x^{2}-16}}dx
tangent of y=7+5x^2-2x^3,(2,11)	tangent\:y=7+5x^{2}-2x^{3},(2,11)
limit as x approaches 2 of (x+4)/(x-2)	\lim\:_{x\to\:2}(\frac{x+4}{x-2})
derivative of ln(cos(1/x))	\frac{d}{dx}(\ln(\cos(\frac{1}{x})))
(dy)/(dx)=e^{5x}+8y	\frac{dy}{dx}=e^{5x}+8y
y^3-(2x+4)+3xy^2y^'=0	y^{3}-(2x+4)+3xy^{2}y^{\prime\:}=0
7cos(2x),7sin(4x),x=0,x= pi/4	7\cos(2x),7\sin(4x),x=0,x=\frac{π}{4}
tangent of 2x^3+3x^2-12x+2	tangent\:2x^{3}+3x^{2}-12x+2
(\partial)/(\partial x)(sin(t))	\frac{\partial\:}{\partial\:x}(\sin(t))
integral of 1/(sqrt(-t^2+4t-3))	\int\:\frac{1}{\sqrt{-t^{2}+4t-3}}dt
derivative of ln(cos(3x))	derivative\:\ln(\cos(3x))
derivative of x*e^{-2x^2}	\frac{d}{dx}(x\cdot\:e^{-2x^{2}})
integral of 1/(5-3x)	\int\:\frac{1}{5-3x}dx
derivative of-e^{-x}+1/3	\frac{d}{dx}(-e^{-x}+\frac{1}{3})
integral from 2 to infinity of-6x^{-2}	\int\:_{2}^{\infty\:}-6x^{-2}dx
integral of 1/((x-6)sqrt(x^2-12x))	\int\:\frac{1}{(x-6)\sqrt{x^{2}-12x}}dx
(dy)/(dx)+(2xy^2)=0	\frac{dy}{dx}+(2xy^{2})=0
integral from 1 to 8 of x^{-5/3}	\int\:_{1}^{8}x^{-\frac{5}{3}}dx
tangent of e^x(7-5x+3x^2),\at x=0	tangent\:e^{x}(7-5x+3x^{2}),\at\:x=0
integral of 6sec^6(x)	\int\:6\sec^{6}(x)dx
derivative of h(x)=(2/x-3)(x^2+7)	derivative\:h(x)=(\frac{2}{x}-3)(x^{2}+7)
limit as x approaches 0 of ln((1+x)/x)	\lim\:_{x\to\:0}(\ln(\frac{1+x}{x}))
integral of (x^2cos(x))	\int\:(x^{2}\cos(x))dx
integral of sin((n*pi)/3 x)	\int\:\sin(\frac{n\cdot\:π}{3}x)dx
integral of y/(1+xy)	\int\:\frac{y}{1+xy}dx
slope of y=1-x^2,x=2	slope\:y=1-x^{2},x=2
derivative of (sqrt(x))/(4x+8)	derivative\:\frac{\sqrt{x}}{4x+8}
derivative of \sqrt[8]{x}	derivative\:\sqrt[8]{x}
(x^2-9)(dy)/(dx)+6y=(x+3)^2	(x^{2}-9)\frac{dy}{dx}+6y=(x+3)^{2}
limit as x approaches 1+of (x-4)/(1-x)	\lim\:_{x\to\:1+}(\frac{x-4}{1-x})
(\partial)/(\partial x)(e^{x-1})	\frac{\partial\:}{\partial\:x}(e^{x-1})
laplacetransform 5e^{3t}	laplacetransform\:5e^{3t}
integral of x/(sqrt(x^2+3))	\int\:\frac{x}{\sqrt{x^{2}+3}}dx
(\partial)/(\partial x)(tan(ln(x*y)))	\frac{\partial\:}{\partial\:x}(\tan(\ln(x\cdot\:y)))
derivative of cos(e^{3x^2})	\frac{d}{dx}(\cos(e^{3x^{2}}))
integral of (1+x)^4	\int\:(1+x)^{4}dx
integral of-2x^2	\int\:-2x^{2}dx
integral from 7/6 to 6 of 1/(1-x^2)	\int\:_{\frac{7}{6}}^{6}\frac{1}{1-x^{2}}dx
derivative of 9x^2cos(x)cot(x)	derivative\:9x^{2}\cos(x)\cot(x)
tangent of f(x)= 7/(sqrt(x)),(4, 7/2)	tangent\:f(x)=\frac{7}{\sqrt{x}},(4,\frac{7}{2})
(dy)/(dx)-2y=e^{5x}	\frac{dy}{dx}-2y=e^{5x}
derivative of-5sin(2x)	\frac{d}{dx}(-5\sin(2x))
derivative of cos(x+1)	\frac{d}{dx}(\cos(x+1))
x^2y^{''}-4xy^'-36y=0	x^{2}y^{\prime\:\prime\:}-4xy^{\prime\:}-36y=0
(\partial)/(\partial x)(xycos(3x)+e^{xy})	\frac{\partial\:}{\partial\:x}(xy\cos(3x)+e^{xy})
(x+1)y^'-y=x	(x+1)y^{\prime\:}-y=x
integral of (2x^5)	\int\:(2x^{5})dx
(xdy)/(dx)+y=-8xy^2,y(1)=5	\frac{xdy}{dx}+y=-8xy^{2},y(1)=5
derivative of f(x)= x/4 arcsin(x)	derivative\:f(x)=\frac{x}{4}\arcsin(x)
xy^'+y=x^3	xy^{\prime\:}+y=x^{3}
integral of (x+1)/(x^2+2x-3)	\int\:\frac{x+1}{x^{2}+2x-3}dx
(\partial)/(\partial x)(x^3+8y^3-6xy+5)	\frac{\partial\:}{\partial\:x}(x^{3}+8y^{3}-6xy+5)
limit as x approaches-1-of x^3-3	\lim\:_{x\to\:-1-}(x^{3}-3)
derivative of 3ax^2+2bx+c	\frac{d}{dx}(3ax^{2}+2bx+c)
integral of (4x^2-2)x	\int\:(4x^{2}-2)xdx
tangent of y=sin(sin(x)),(3pi,0)	tangent\:y=\sin(\sin(x)),(3π,0)
(\partial)/(\partial x)(sin(x^2-5xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}-5xy))
integral of 1/(3x)	\int\:\frac{1}{3x}dx
derivative of (e^{(x^2}+4)^2(4x)^3x)	\frac{d}{dx}((e^{(x^{2})}+4)^{2}(4x)^{3}x)
integral of 1/(sin(x)cos^3(x))	\int\:\frac{1}{\sin(x)\cos^{3}(x)}dx
integral from 3 to 4 of ((2x-3))/6	\int\:_{3}^{4}\frac{(2x-3)}{6}dx
sqrt(1-9x^2)y^'=x	\sqrt{1-9x^{2}}y^{\prime\:}=x
derivative of (\|x\|/(sqrt(2-x^2)))	\frac{d}{dx}(\frac{\left\|x\right\|}{\sqrt{2-x^{2}}})
(dy)/(dt)+5y=5	\frac{dy}{dt}+5y=5
3(1+t^2)((dy)/(dt))=2ty(y^3-1)	3(1+t^{2})(\frac{dy}{dt})=2ty(y^{3}-1)
y^{''}+81y=-81sec^2(9x)	y^{\prime\:\prime\:}+81y=-81\sec^{2}(9x)

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