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Popular Calculus Problems

limit as x approaches 0+of (1/x)^{x^2}	\lim\:_{x\to\:0+}((\frac{1}{x})^{x^{2}})
derivative of arccsc(x)	derivative\:\arccsc(x)
limit as x approaches 2 of x^3-2x^2+x+1	\lim\:_{x\to\:2}(x^{3}-2x^{2}+x+1)
integral from-infinity to 0 of e^{rx}	\int\:_{-\infty\:}^{0}e^{rx}dx
integral of 8e^{x/2}	\int\:8e^{\frac{x}{2}}dx
derivative of (e^x+e^{-x}/5)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{5})
derivative of xcos(2x)	derivative\:x\cos(2x)
limit as x approaches+4 of (4-x)/(\|4-x\|)	\lim\:_{x\to\:+4}(\frac{4-x}{\left\|4-x\right\|})
integral of y^2-1	\int\:y^{2}-1dy
integral from 0 to y of 2(x+y)	\int\:_{0}^{y}2(x+y)dx
integral of (2x^3+8x-4)/(x^4+4x^2)	\int\:\frac{2x^{3}+8x-4}{x^{4}+4x^{2}}dx
tangent of f(x)=-0.025x^2	tangent\:f(x)=-0.025x^{2}
integral from 21 to infinity of xe^{-x}	\int\:_{21}^{\infty\:}xe^{-x}dx
derivative of 14ln(x)	\frac{d}{dx}(14\ln(x))
derivative of x^2+x-5	derivative\:x^{2}+x-5
integral from 1 to 2 of 1/x	\int\:_{1}^{2}\frac{1}{x}dx
(\partial)/(\partial x)(3xyz)	\frac{\partial\:}{\partial\:x}(3xyz)
sum from n=1 to infinity of 2^n(n!)^2	\sum\:_{n=1}^{\infty\:}2^{n}(n!)^{2}
integral from 1 to 3 of (4x^3-8x+1)	\int\:_{1}^{3}(4x^{3}-8x+1)dx
derivative of 4/x+x^2	\frac{d}{dx}(\frac{4}{x}+x^{2})
integral of 1/(5-3cos(x))	\int\:\frac{1}{5-3\cos(x)}dx
integral of 8e^{4x}(e^{4x}-4)^{1/5}	\int\:8e^{4x}(e^{4x}-4)^{\frac{1}{5}}dx
y^'+1/x y=5x^2	y^{\prime\:}+\frac{1}{x}y=5x^{2}
2y^{''}+26y=0,y(0)=9,y^'(0)=5	2y^{\prime\:\prime\:}+26y=0,y(0)=9,y^{\prime\:}(0)=5
(\partial)/(\partial x)(9x^2+25y^2-225)	\frac{\partial\:}{\partial\:x}(9x^{2}+25y^{2}-225)
implicit (dy)/(dx),6x^3+7y^3=13xy	implicit\:\frac{dy}{dx},6x^{3}+7y^{3}=13xy
slope ofintercept (-1.4)(1.4)	slopeintercept\:(-1.4)(1.4)
derivative of 2arctan(x)-x	derivative\:2\arctan(x)-x
integral of sqrt(sin(x))	\int\:\sqrt{\sin(x)}dx
f(x)=x^4e^x	f(x)=x^{4}e^{x}
limit as x approaches-2+of 2x	\lim\:_{x\to\:-2+}(2x)
integral of e^{2x}(e^{2x}-e^{-2x})	\int\:e^{2x}(e^{2x}-e^{-2x})dx
maclaurin 1/(1-t)	maclaurin\:\frac{1}{1-t}
derivative of (4+2x^2^7)	\frac{d}{dx}((4+2x^{2})^{7})
integral of (4sin(2x)-3cos(3x))	\int\:(4\sin(2x)-3\cos(3x))dx
taylor (2+x)^{-2}	taylor\:(2+x)^{-2}
limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)}	\lim\:_{x\to\:\infty\:}(\frac{2(x-8)^{35}}{(x-1)^{35}})
derivative of f(x)=(sqrt(x)+1)/(x^2+1)	derivative\:f(x)=\frac{\sqrt{x}+1}{x^{2}+1}
(dy)/(dt)=y^3,y(0)=1	\frac{dy}{dt}=y^{3},y(0)=1
derivative of (432/x)	\frac{d}{dx}(\frac{432}{x})
integral of (4x^2-7x-12)/(x(x+2)(x-3))	\int\:\frac{4x^{2}-7x-12}{x(x+2)(x-3)}dx
integral of 4/(x^2(x^2+4))	\int\:\frac{4}{x^{2}(x^{2}+4)}dx
taylor x^3,3	taylor\:x^{3},3
integral of x^{10}e^{x^{11}}	\int\:x^{10}e^{x^{11}}dx
derivative of 7sin^2(x)	\frac{d}{dx}(7\sin^{2}(x))
tangent of f(x)=sqrt(1-3x),\at x=-1	tangent\:f(x)=\sqrt{1-3x},\at\:x=-1
derivative of (3x^2-1/(x-2))	\frac{d}{dx}(\frac{3x^{2}-1}{x-2})
tangent of f(x)=sec(x),\at x=(pi/3)	tangent\:f(x)=\sec(x),\at\:x=(\frac{π}{3})
limit as x approaches-1 of arcos(x)	\lim\:_{x\to\:-1}(ar\cos(x))
integral of (2+3cos(x))/(sin^2(x))	\int\:\frac{2+3\cos(x)}{\sin^{2}(x)}dx
integral of 1/(sqrt(20+8x-x^2))	\int\:\frac{1}{\sqrt{20+8x-x^{2}}}dx
integral from 0 to 2 of 2x	\int\:_{0}^{2}2xdx
inverse oflaplace (s+5)/(s^2+6s+18)	inverselaplace\:\frac{s+5}{s^{2}+6s+18}
y^{''}-6y^'+9y=6x^2+2-12e^{3x}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=6x^{2}+2-12e^{3x}
tangent of (3+sin(2x))^2,\at x=0	tangent\:(3+\sin(2x))^{2},\at\:x=0
taylor 2/(x^2-x)	taylor\:\frac{2}{x^{2}-x}
integral of 2x+8x^{-2}	\int\:2x+8x^{-2}dx
tangent of f(x)=x^2+10x,\at x=8	tangent\:f(x)=x^{2}+10x,\at\:x=8
limit as x approaches infinity of x^2e^{2x}	\lim\:_{x\to\:\infty\:}(x^{2}e^{2x})
limit as x approaches-2 of (x^3+1)/(x+1)	\lim\:_{x\to\:-2}(\frac{x^{3}+1}{x+1})
y^{''}-3y^'+2y=14sin(2x)+18cos(2x)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=14\sin(2x)+18\cos(2x)
derivative of 3x^5-2x^4-4x^3	\frac{d}{dx}(3x^{5}-2x^{4}-4x^{3})
(y-sqrt(x^2+y^2))dx-xdy=0	(y-\sqrt{x^{2}+y^{2}})dx-xdy=0
derivative of xln(x^6)	\frac{d}{dx}(x\ln(x^{6}))
tangent of f(x)=110x-16x^2,\at 3	tangent\:f(x)=110x-16x^{2},\at\:3
derivative of 7x	derivative\:7x
(dx)/(dt)=(((e^tx+1))/(1-e^t))	\frac{dx}{dt}=(\frac{(e^{t}x+1)}{1-e^{t}})
integral of (x-3)/((x+4)(x+5))	\int\:\frac{x-3}{(x+4)(x+5)}dx
derivative of csc(θ)	derivative\:\csc(θ)
integral from pi to 2pi of xsin(x/2)	\int\:_{π}^{2π}x\sin(\frac{x}{2})dx
y^{''}+12y^'+36y=t^{-2}e^{-6t}	y^{\prime\:\prime\:}+12y^{\prime\:}+36y=t^{-2}e^{-6t}
y^{''}-2y^'+2y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=0
tangent of y=4-x^2,(-1,3)	tangent\:y=4-x^{2},(-1,3)
inverse oflaplace 1/(3s+1)	inverselaplace\:\frac{1}{3s+1}
y^{''}+14y^'+49y=t^{-2}e^{-7t}	y^{\prime\:\prime\:}+14y^{\prime\:}+49y=t^{-2}e^{-7t}
integral of (z+2)^2	\int\:(z+2)^{2}dz
derivative of sqrt(cos(2^x*x^5))	\frac{d}{dx}(\sqrt{\cos(2^{x}\cdot\:x^{5})})
derivative of sqrt(9+\sqrt{9-x)}	\frac{d}{dx}(\sqrt{9+\sqrt{9-x}})
integral of (15sqrt(x)+sqrt(2))	\int\:(15\sqrt{x}+\sqrt{2})dx
limit as x approaches-3+of 8x+5	\lim\:_{x\to\:-3+}(8x+5)
integral of 1/(4y^2+1)	\int\:\frac{1}{4y^{2}+1}dy
(\partial)/(\partial x)(xln(1+x+y))	\frac{\partial\:}{\partial\:x}(x\ln(1+x+y))
integral from 0 to 1 of x	\int\:_{0}^{1}xdx
derivative of e^x(7x^2-14x+14)	derivative\:e^{x}(7x^{2}-14x+14)
tangent of 4/(x^2)-1/(sqrt(x))	tangent\:\frac{4}{x^{2}}-\frac{1}{\sqrt{x}}
(d^2)/(dx^2)(1/(sqrt(1-x^2)))	\frac{d^{2}}{dx^{2}}(\frac{1}{\sqrt{1-x^{2}}})
integral of 2yarctan(x)	\int\:2y\arctan(x)dy
y^{''}-2y^'-24y=0,y(0)=-1,y^'(0)=14	y^{\prime\:\prime\:}-2y^{\prime\:}-24y=0,y(0)=-1,y^{\prime\:}(0)=14
integral of ((x^3))/((sqrt(x^4+5)))	\int\:\frac{(x^{3})}{(\sqrt{x^{4}+5})}dx
integral of 6/(sec(2x)-1)	\int\:\frac{6}{\sec(2x)-1}dx
integral of (a-by)^4	\int\:(a-by)^{4}dy
limit as x approaches 5+of x^2+2x-3	\lim\:_{x\to\:5+}(x^{2}+2x-3)
(\partial)/(\partial y)(sin(2y+x)sin(x))	\frac{\partial\:}{\partial\:y}(\sin(2y+x)\sin(x))
sum from n=0 to infinity of 3n-1	\sum\:_{n=0}^{\infty\:}3n-1
integral of (12)/(1-cos(3x))	\int\:\frac{12}{1-\cos(3x)}dx
(\partial)/(\partial y)(4x^3-4x)	\frac{\partial\:}{\partial\:y}(4x^{3}-4x)
derivative of 3^{2x+1}	derivative\:3^{2x+1}
integral of 1/(7x-2)	\int\:\frac{1}{7x-2}dx
limit as x approaches 3-of sqrt(x-3)	\lim\:_{x\to\:3-}(\sqrt{x-3})
limit as x approaches 1 of (x+9)/(x+1)	\lim\:_{x\to\:1}(\frac{x+9}{x+1})

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