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Popular Calculus Problems

sum from n=0 to infinity of (1.67)^n	\sum\:_{n=0}^{\infty\:}(1.67)^{n}
implicit (dy)/(dx),y^9=x^8	implicit\:\frac{dy}{dx},y^{9}=x^{8}
integral of (x^2-8)^3(2x)	\int\:(x^{2}-8)^{3}(2x)dx
integral from 1 to infinity of x^{-7}	\int\:_{1}^{\infty\:}x^{-7}dx
derivative of (x+2/(x^2+4x+13))	\frac{d}{dx}(\frac{x+2}{x^{2}+4x+13})
sum from n=1 to infinity of (60)/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{60}{7^{n}}
f(t)=sin(t)+tcos(t)	f(t)=\sin(t)+t\cos(t)
(\partial)/(\partial y)((x^2+y^2+z^2)^{-1/2})	\frac{\partial\:}{\partial\:y}((x^{2}+y^{2}+z^{2})^{-\frac{1}{2}})
integral of sin^3(8xco)s^{-2}8x	\int\:\sin^{3}(8xco)s^{-2}8xdx
derivative of f(x)=sin^2(tan(sqrt(x)))	derivative\:f(x)=\sin^{2}(\tan(\sqrt{x}))
sum from n=1 to infinity of (e/pi)^n	\sum\:_{n=1}^{\infty\:}(\frac{e}{π})^{n}
tangent of y=x^3,(1,1)	tangent\:y=x^{3},(1,1)
d/(dt)(-1/(t+1))	\frac{d}{dt}(-\frac{1}{t+1})
derivative of (x/(x+1)^5)	\frac{d}{dx}((\frac{x}{x+1})^{5})
limit as t approaches 0 of (sin(kt))/t	\lim\:_{t\to\:0}(\frac{\sin(kt)}{t})
derivative of f(x)= x/a	derivative\:f(x)=\frac{x}{a}
tangent of f(x)=x^2(4-x)^2,\at x=1	tangent\:f(x)=x^{2}(4-x)^{2},\at\:x=1
integral from 0 to 1 of 1/(1-x^2)	\int\:_{0}^{1}\frac{1}{1-x^{2}}dx
limit as x approaches 0 of 3/(e^x+1)	\lim\:_{x\to\:0}(\frac{3}{e^{x}+1})
(\partial)/(\partial x)(6x^2+7y)	\frac{\partial\:}{\partial\:x}(6x^{2}+7y)
derivative of \|x\|^3-x^2	\frac{d}{dx}(\left\|x\right\|^{3}-x^{2})
limit as x approaches infinity of sqrt((12x^3-4x+1)/(1+3x+2x^3))	\lim\:_{x\to\:\infty\:}(\sqrt{\frac{12x^{3}-4x+1}{1+3x+2x^{3}}})
derivative of (8x-7)/(5x+12)	derivative\:\frac{8x-7}{5x+12}
derivative of {f}(x(x)^{-1}(ax))	\frac{d}{dx}({f}(x)(x)^{-1}(ax))
d/(dt)(t^2-1)	\frac{d}{dt}(t^{2}-1)
integral of (sin(x))/(2e^x)	\int\:\frac{\sin(x)}{2e^{x}}dx
integral from-3 to 3 of \|x\|-(x^2-6)	\int\:_{-3}^{3}\left\|x\right\|-(x^{2}-6)dx
inverse oflaplace-1/2*1/((x^2+1)^2)	inverselaplace\:-\frac{1}{2}\cdot\:\frac{1}{(x^{2}+1)^{2}}
integral from 0 to 2 of (2x-x^2)^2	\int\:_{0}^{2}(2x-x^{2})^{2}dx
integral from 5 to 6 of x/(x-5)	\int\:_{5}^{6}\frac{x}{x-5}dx
integral of (x^2)/(x+5)	\int\:\frac{x^{2}}{x+5}dx
area x=9y^3,x=9y^2	area\:x=9y^{3},x=9y^{2}
derivative of sin(xln(3x))	\frac{d}{dx}(\sin(x)\ln(3x))
integral of (x-3)/(x^3+3x^2+2x)	\int\:\frac{x-3}{x^{3}+3x^{2}+2x}dx
integral of e^{-(2r)/a}	\int\:e^{-\frac{2r}{a}}dr
limit as x approaches-9 of (x+10)/(x+9)	\lim\:_{x\to\:-9}(\frac{x+10}{x+9})
integral of (2x+3)^{-3}	\int\:(2x+3)^{-3}dx
derivative of (5x^2+e^x/(x^3))	\frac{d}{dx}(\frac{5x^{2}+e^{x}}{x^{3}})
derivative of 1/(1-4x)	\frac{d}{dx}(\frac{1}{1-4x})
derivative of (x^2/(3x-4))	\frac{d}{dx}(\frac{x^{2}}{3x-4})
limit as x approaches-5 of f(x)	\lim\:_{x\to\:-5}(f(x))
integral of 2x^5	\int\:2x^{5}dx
integral from 0 to x of (2t^2+sqrt(t))	\int\:_{0}^{x}(2t^{2}+\sqrt{t})dt
limit as x approaches infinity of x_{1}	\lim\:_{x\to\:\infty\:}(x_{1})
integral of (8-x)	\int\:(8-x)dx
derivative of f(x)=sqrt(x^2-1)	derivative\:f(x)=\sqrt{x^{2}-1}
area 7x-x^2,2x,(0,10)	area\:7x-x^{2},2x,(0,10)
derivative of x(4x-12)^3	derivative\:x(4x-12)^{3}
integral of 5sin(5x)sin(x)	\int\:5\sin(5x)\sin(x)dx
integral of (x^3)/((9-x^4)^2)	\int\:\frac{x^{3}}{(9-x^{4})^{2}}dx
derivative of f(x)=2x^e	derivative\:f(x)=2x^{e}
integral of 4x+3x^2+12x^3+C	\int\:4x+3x^{2}+12x^{3}+Cdx
integral of (cos(pix))/(sin(pix))	\int\:\frac{\cos(π\cdot\:x)}{\sin(π\cdot\:x)}dx
(dy)/(dx)=e^{2x+y}	\frac{dy}{dx}=e^{2x+y}
(dy)/(dx)=xe^{x^2-ln(y^2)}	\frac{dy}{dx}=xe^{x^{2}-\ln(y^{2})}
integral from-2 to 3 of (10x^3-4x)(x+2)	\int\:_{-2}^{3}(10x^{3}-4x)(x+2)dx
derivative of f(x)=xsin(2/x)	derivative\:f(x)=x\sin(\frac{2}{x})
limit as x approaches 2+of 2-x^2	\lim\:_{x\to\:2+}(2-x^{2})
derivative of-6/(x^2)-5/x	derivative\:-\frac{6}{x^{2}}-\frac{5}{x}
limit as x approaches 2 of x^2-x-2	\lim\:_{x\to\:2}(x^{2}-x-2)
limit as x approaches-2 of 1	\lim\:_{x\to\:-2}(1)
integral of (2+x^2)/(sqrt(x))	\int\:\frac{2+x^{2}}{\sqrt{x}}dx
(\partial)/(\partial x)(cos(2y-3x))	\frac{\partial\:}{\partial\:x}(\cos(2y-3x))
integral of (2x+1)ln(x+1)	\int\:(2x+1)\ln(x+1)dx
(\partial)/(\partial x)(1/(1+e))	\frac{\partial\:}{\partial\:x}(\frac{1}{1+e})
integral of x/(2y^4)	\int\:\frac{x}{2y^{4}}dx
derivative of (3sin(x)/(2+cos(x)))	\frac{d}{dx}(\frac{3\sin(x)}{2+\cos(x)})
integral from 0 to 2 of 4t	\int\:_{0}^{2}4tdt
integral of 3/(x^{3/4)}-4\sqrt[3]{x}+1	\int\:\frac{3}{x^{\frac{3}{4}}}-4\sqrt[3]{x}+1dx
derivative of f(x)=(4x-3)/(5x^2+3x)	derivative\:f(x)=\frac{4x-3}{5x^{2}+3x}
integral of xsin^3(x)	\int\:x\sin^{3}(x)dx
integral of x^2arctan(x)	\int\:x^{2}\arctan(x)dx
derivative of x^3-4x	\frac{d}{dx}(x^{3}-4x)
(d^3)/(dx^3)(7/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{7}{x^{2}})
(\partial)/(\partial x)(a^x)	\frac{\partial\:}{\partial\:x}(a^{x})
integral of (5x)/((x^2+5)^2)	\int\:\frac{5x}{(x^{2}+5)^{2}}dx
derivative of-cos(x/2)	\frac{d}{dx}(-\cos(\frac{x}{2}))
tangent of (-6x)/((x^2+1))	tangent\:\frac{-6x}{(x^{2}+1)}
derivative of (sin^2(x)/(1+cos^2(x)))	\frac{d}{dx}(\frac{\sin^{2}(x)}{1+\cos^{2}(x)})
integral of 1/((4x+5)^2)	\int\:\frac{1}{(4x+5)^{2}}dx
tangent of (8x)/((x+1)^2)	tangent\:\frac{8x}{(x+1)^{2}}
integral of 1/((y^2+1))	\int\:\frac{1}{(y^{2}+1)}dy
derivative of cos((1-e^{2x}/(1+e^{2x)}))	\frac{d}{dx}(\cos(\frac{1-e^{2x}}{1+e^{2x}}))
derivative of F(r)= 7/(r^3)	derivative\:F(r)=\frac{7}{r^{3}}
integral from 0 to 1 of 5ln(4x)	\int\:_{0}^{1}5\ln(4x)dx
area sqrt(x)+3, 1/2 x+3	area\:\sqrt{x}+3,\frac{1}{2}x+3
(dx)/(dt)=xe^t-3e^t+x-3	\frac{dx}{dt}=xe^{t}-3e^{t}+x-3
integral from 0 to 60 of 60e^{-0.02x}	\int\:_{0}^{60}60e^{-0.02x}dx
slope of (0,-9),(4,-10)	slope\:(0,-9),(4,-10)
derivative of sin(\sqrt[3]{x}+\sqrt[3]{sin(x)})	\frac{d}{dx}(\sin(\sqrt[3]{x})+\sqrt[3]{\sin(x)})
derivative of 6(6+(18)/(x^3))	derivative\:6(6+\frac{18}{x^{3}})
(\partial)/(\partial y)(e^{-x-y})	\frac{\partial\:}{\partial\:y}(e^{-x-y})
tangent of f(x)=sqrt(7x+1),\at x=9	tangent\:f(x)=\sqrt{7x+1},\at\:x=9
sum from n=0 to infinity of 3/(n(n+3))	\sum\:_{n=0}^{\infty\:}\frac{3}{n(n+3)}
integral of (2x+1)/(x^6+18x^4+81x^2)	\int\:\frac{2x+1}{x^{6}+18x^{4}+81x^{2}}dx
sum from n=1 to infinity of 5/(n^2+9n+7)	\sum\:_{n=1}^{\infty\:}\frac{5}{n^{2}+9n+7}
limit as x approaches pi/2 of xsin(x)	\lim\:_{x\to\:\frac{π}{2}}(x\sin(x))
derivative of e^{2.4}	\frac{d}{dx}(e^{2.4})
integral of (x^3sin(npix))	\int\:(x^{3}\sin(nπx))dx
((log_{10}(x))/x)^'	(\frac{\log_{10}(x)}{x})^{\prime\:}

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