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Popular Calculus Problems

limit as x approaches 1 of 3x^2-1	\lim\:_{x\to\:1}(3x^{2}-1)
integral of 1/5 e^{-x/5}	\int\:\frac{1}{5}e^{-\frac{x}{5}}dx
integral of (2+tan^2(x))	\int\:(2+\tan^{2}(x))dx
(d^2x)/(dt^2)+4x=cos(3t)	\frac{d^{2}x}{dt^{2}}+4x=\cos(3t)
limit as x approaches 2 of 4-a*x	\lim\:_{x\to\:2}(4-a\cdot\:x)
sum from n=0 to infinity of 3x^n	\sum\:_{n=0}^{\infty\:}3x^{n}
derivative of (7-xe^x)/(x+e^x)	derivative\:\frac{7-xe^{x}}{x+e^{x}}
integral of (xy^2+x^2+y+4)	\int\:(xy^{2}+x^{2}+y+4)dx
derivative of f(v)=(v^{-3}+3v^{-2})^3	derivative\:f(v)=(v^{-3}+3v^{-2})^{3}
f(x)=xsqrt(5-x)	f(x)=x\sqrt{5-x}
limit as x approaches 4+of x^3-cx	\lim\:_{x\to\:4+}(x^{3}-cx)
integral of e^{-0.02x}(e^{-0.13x}+4)	\int\:e^{-0.02x}(e^{-0.13x}+4)dx
integral of 1/((x^2+x)(x-1)^2)	\int\:\frac{1}{(x^{2}+x)(x-1)^{2}}dx
integral of ((5x^4+x^3-x^2+x+3)/(x^2))	\int\:(\frac{5x^{4}+x^{3}-x^{2}+x+3}{x^{2}})dx
derivative of sin(picos(x))	\frac{d}{dx}(\sin(π\cos(x)))
integral of 7^{3x}	\int\:7^{3x}dx
integral of (x+sqrt(x))^2	\int\:(x+\sqrt{x})^{2}dx
limit as x approaches 2 of e^x-1	\lim\:_{x\to\:2}(e^{x}-1)
derivative of (cos(x)/(x^3))	\frac{d}{dx}(\frac{\cos(x)}{x^{3}})
integral of r^2-x^2	\int\:r^{2}-x^{2}dx
y^{''}+4y=sec(2x)	y^{\prime\:\prime\:}+4y=\sec(2x)
derivative of-(15/(16x^{7/2)})	\frac{d}{dx}(-\frac{15}{16x^{\frac{7}{2}}})
limit as x approaches 0 of (sin^3(x))/x	\lim\:_{x\to\:0}(\frac{\sin^{3}(x)}{x})
derivative of (3x)/(sqrt(x^2+3))	derivative\:\frac{3x}{\sqrt{x^{2}+3}}
y^'= x/(3y)	y^{\prime\:}=\frac{x}{3y}
integral of 6/(1-cos(3x))	\int\:\frac{6}{1-\cos(3x)}dx
integral from 0 to 1 of xsqrt(x^2+8)	\int\:_{0}^{1}x\sqrt{x^{2}+8}dx
derivative of 3sqrt(x)sin(x)	derivative\:3\sqrt{x}\sin(x)
integral of x^3-x	\int\:x^{3}-xdx
(\partial)/(\partial x)(sqrt(5x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{5x^{2}+y^{2}})
integral of 3cos(x/2)	\int\:3\cos(\frac{x}{2})dx
integral of 1/((8-x)^2)	\int\:\frac{1}{(8-x)^{2}}dx
integral of x^9cos(x^5)	\int\:x^{9}\cos(x^{5})dx
integral of (4csc(x)cot(x)+2sec^2(x))	\int\:(4\csc(x)\cot(x)+2\sec^{2}(x))dx
derivative of f(x)=20x^2+14x-2x^2	derivative\:f(x)=20x^{2}+14x-2x^{2}
derivative of arccos((10/x))	\frac{d}{dx}(\arccos(\frac{10}{x}))
derivative of f(x)=e^x-6x^5	derivative\:f(x)=e^{x}-6x^{5}
derivative of 2+sqrt(3+cos^2(x))	derivative\:2+\sqrt{3+\cos^{2}(x)}
(\partial)/(\partial x)(ln(y^{x^2}))	\frac{\partial\:}{\partial\:x}(\ln(y^{x^{2}}))
ty^'+4y=0	ty^{\prime\:}+4y=0
integral of 1/(y^2+3)	\int\:\frac{1}{y^{2}+3}dy
sum from n=0 to infinity of n(z-1)^{n-1}	\sum\:_{n=0}^{\infty\:}n(z-1)^{n-1}
(\partial)/(\partial t)(6q(r,t)^2+7r^3-8/t-q(r,t)t)	\frac{\partial\:}{\partial\:t}(6q(r,t)^{2}+7r^{3}-\frac{8}{t}-q(r,t)t)
sum from n=0 to infinity of 2/(n^2+6n+8)	\sum\:_{n=0}^{\infty\:}\frac{2}{n^{2}+6n+8}
derivative of (2x-5)^2	derivative\:(2x-5)^{2}
taylor x^2cos(x)	taylor\:x^{2}\cos(x)
derivative of sin^3(2x)	derivative\:\sin^{3}(2x)
derivative of (2x^2+6x+8/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+6x+8}{\sqrt{x}})
(\partial)/(\partial z)(xye^x)	\frac{\partial\:}{\partial\:z}(xye^{x})
(\partial)/(\partial x)((2t-1)(3t-6)^{-1})	\frac{\partial\:}{\partial\:x}((2t-1)(3t-6)^{-1})
integral of (sqrt(x)+1)/(sqrt(x))	\int\:\frac{\sqrt{x}+1}{\sqrt{x}}dx
derivative of by(x^2)	\frac{d}{dx}(by(x)^{2})
integral of (1+2x)^4(2)	\int\:(1+2x)^{4}(2)dx
inverse oflaplace (s-9)/(s^2-9)	inverselaplace\:\frac{s-9}{s^{2}-9}
derivative of sqrt(tan(4x))	\frac{d}{dx}(\sqrt{\tan(4x)})
(dy)/(dx)+y/(x-2)=5(x-2)y^{1/2}	\frac{dy}{dx}+\frac{y}{x-2}=5(x-2)y^{\frac{1}{2}}
derivative of f(x)=(6x^2-1)/(2sqrt(x))	derivative\:f(x)=\frac{6x^{2}-1}{2\sqrt{x}}
derivative of 1/(2x^2+1)	\frac{d}{dx}(\frac{1}{2x^{2}+1})
derivative of cos^2(e^x+sqrt(x))	derivative\:\cos^{2}(e^{x}+\sqrt{x})
(\partial)/(\partial y)(-e^{x-y}x)	\frac{\partial\:}{\partial\:y}(-e^{x-y}x)
integral of xcos(8x^2+pi)	\int\:x\cos(8x^{2}+π)dx
integral of-9cos(3x+pi)	\int\:-9\cos(3x+π)dx
(\partial)/(\partial s)((t^2)/(s^3))	\frac{\partial\:}{\partial\:s}(\frac{t^{2}}{s^{3}})
derivative of (2x^3+5)^4	derivative\:(2x^{3}+5)^{4}
integral of (x^2+5x)cos(x)	\int\:(x^{2}+5x)\cos(x)dx
(dy)/(dx)=0.5y	\frac{dy}{dx}=0.5y
limit as x approaches 0+of (\|2x\|)/x	\lim\:_{x\to\:0+}(\frac{\left\|2x\right\|}{x})
limit as n approaches infinity of Arg(-1+i/n)	\lim\:_{n\to\:\infty\:}(Arg(-1+\frac{i}{n}))
inverse oflaplace (0.5)/(s*(s^2+s+1))	inverselaplace\:\frac{0.5}{s\cdot\:(s^{2}+s+1)}
(dx)/(dt)-(tan(t))x=sin(t),x(0)=1	\frac{dx}{dt}-(\tan(t))x=\sin(t),x(0)=1
limit as x approaches 0 of x/(x^2+7x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+7x})
derivative of (\|x-2\|/(x^2))	\frac{d}{dx}(\frac{\left\|x-2\right\|}{x^{2}})
integral from-3 to 5 of 6-y-((y-3)^2)/4	\int\:_{-3}^{5}6-y-\frac{(y-3)^{2}}{4}dy
derivative of f(x)=7tan^3(x)	derivative\:f(x)=7\tan^{3}(x)
derivative of 16^x	derivative\:16^{x}
integral of+(16)/((64x^2+1)^2)	\int\:+\frac{16}{(64x^{2}+1)^{2}}dx
(dy)/(dx)-cos(x)y= 1/100 cos(x)	\frac{dy}{dx}-\cos(x)y=\frac{1}{100}\cos(x)
integral of sin(x^2)x	\int\:\sin(x^{2})xdx
limit as x approaches 2 of x-1	\lim\:_{x\to\:2}(x-1)
derivative of-10x	derivative\:-10x
integral of 7xe^{8x}	\int\:7xe^{8x}dx
derivative of ((x+6/(x-6))^5)	\frac{d}{dx}((\frac{x+6}{x-6})^{5})
area x=-5,x=3,y=2x^2+12,y=0	area\:x=-5,x=3,y=2x^{2}+12,y=0
integral of 1/((x-2)(x-5))	\int\:\frac{1}{(x-2)(x-5)}dx
(\partial)/(\partial x)(3x^2+2xy-7y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}+2xy-7y^{2})
f^'(x)=sqrt(x)	f^{\prime\:}(x)=\sqrt{x}
derivative of sqrt(1+x^4)	\frac{d}{dx}(\sqrt{1+x^{4}})
derivative of ln(sqrt(((2x+1))/(x^2-3)))	derivative\:\ln(\sqrt{\frac{(2x+1)}{x^{2}-3}})
integral of xln(x^2)	\int\:x\ln(x^{2})dx
derivative of x^3Inx	\frac{d}{dx}(x^{3}Inx)
limit as x approaches 0 of x-1/(x-1)	\lim\:_{x\to\:0}(x-\frac{1}{x-1})
integral of 100e^{0.2x}	\int\:100e^{0.2x}dx
integral from 4 to 9 of (x-sqrt(x))/x	\int\:_{4}^{9}\frac{x-\sqrt{x}}{x}dx
integral of e^{2x-2}	\int\:e^{2x-2}dx
derivative of 1/(2x^2-3)	\frac{d}{dx}(\frac{1}{2x^{2}-3})
integral of ((e^{x^2}-1))/x	\int\:\frac{(e^{x^{2}}-1)}{x}dx
integral from 0 to 1 of 1/((x-1)^2)	\int\:_{0}^{1}\frac{1}{(x-1)^{2}}dx
taylor (sqrt(1+x))/(sqrt(1-x))	taylor\:\frac{\sqrt{1+x}}{\sqrt{1-x}}
integral of 1/((1-y^2)^{1/2)}	\int\:\frac{1}{(1-y^{2})^{\frac{1}{2}}}dy
integral of (x+1)/(x^2+2x+2)	\int\:\frac{x+1}{x^{2}+2x+2}dx

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