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Popular Calculus Problems

integral from 0 to 5 of x/(sqrt(1+4x))	\int\:_{0}^{5}\frac{x}{\sqrt{1+4x}}dx
integral of (2x^3-3x^2-3x+2)/(x-2)	\int\:\frac{2x^{3}-3x^{2}-3x+2}{x-2}dx
integral from 0 to 2 of x-1	\int\:_{0}^{2}x-1dx
x^{''}+2x=0,x(0)=1,x(1)=0	x^{\prime\:\prime\:}+2x=0,x(0)=1,x(1)=0
derivative of 13440(2x+5)^3	derivative\:13440(2x+5)^{3}
slope of y=x^2-2x-2P(y,x),(2,-2)	slope\:y=x^{2}-2x-2P(y,x),(2,-2)
limit as x approaches 0 of x/(sin(2x))	\lim\:_{x\to\:0}(\frac{x}{\sin(2x)})
limit as x approaches 1 of sin(pi/x)	\lim\:_{x\to\:1}(\sin(\frac{π}{x}))
sum from n=1 to infinity of n/(10n+12)	\sum\:_{n=1}^{\infty\:}\frac{n}{10n+12}
area (2)sin(x),[0,pi]	area\:(2)\sin(x),[0,π]
integral of ((x^2-x+12))/((x^3+3x))	\int\:\frac{(x^{2}-x+12)}{(x^{3}+3x)}dx
integral of 2-y	\int\:2-ydy
taylor 1/(x^2),7	taylor\:\frac{1}{x^{2}},7
derivative of x^{5/2}e^x	derivative\:x^{\frac{5}{2}}e^{x}
limit as x approaches 9+of 2/(x+9)	\lim\:_{x\to\:9+}(\frac{2}{x+9})
derivative of e^{x+2}+2	derivative\:e^{x+2}+2
integral of-7/5 x^{-12}	\int\:-\frac{7}{5}x^{-12}dx
derivative of e^{cos(x}sin(x^2-x))	\frac{d}{dx}(e^{\cos(x)}\sin(x^{2}-x))
integral of (3^2+x^{12})	\int\:(3^{2}+x^{12})dx
derivative of x*(ln(x)^2)	\frac{d}{dx}(x\cdot\:(\ln(x))^{2})
inverse oflaplace 1/(s(s^2+4s+3))	inverselaplace\:\frac{1}{s(s^{2}+4s+3)}
integral of 12x^{1/2}	\int\:12x^{\frac{1}{2}}dx
derivative of log_{e}(1/x)	\frac{d}{dx}(\log_{e}(\frac{1}{x}))
integral of (9x^3)/(sqrt(x^2+9))	\int\:\frac{9x^{3}}{\sqrt{x^{2}+9}}dx
derivative of f(x)=x^2+x-3	derivative\:f(x)=x^{2}+x-3
y^'+y=x^2	y^{\prime\:}+y=x^{2}
(17+x^2)y^'-2xy=0	(17+x^{2})y^{\prime\:}-2xy=0
derivative of (cos(x)/(sqrt(1+x^2)))	\frac{d}{dx}(\frac{\cos(x)}{\sqrt{1+x^{2}}})
limit as x approaches 0 of 1/(2x^2)	\lim\:_{x\to\:0}(\frac{1}{2x^{2}})
(d^2)/(dx^2)(cos^2(3pix))	\frac{d^{2}}{dx^{2}}(\cos^{2}(3πx))
integral of x^{28}e^{x^{29}}	\int\:x^{28}e^{x^{29}}dx
integral of ln((1-x)/(1+x))	\int\:\ln(\frac{1-x}{1+x})dx
(d^2)/(dx^2)(3e^{-x^2})	\frac{d^{2}}{dx^{2}}(3e^{-x^{2}})
derivative of (20sin(tw)/(tw))	\frac{d}{dx}(\frac{20\sin(tw)}{tw})
tangent of y=-5-8x^2,(-3,-77)	tangent\:y=-5-8x^{2},(-3,-77)
x(dy)/(dx)+y=11sqrt(x)	x\frac{dy}{dx}+y=11\sqrt{x}
integral of e^{-x/3}	\int\:e^{-\frac{x}{3}}dx
slope ofintercept (4,3),(-2,9)	slopeintercept\:(4,3),(-2,9)
integral of (3x-7)sin(5x+2)	\int\:(3x-7)\sin(5x+2)dx
derivative of (x^2-x/(x^3+x+1))	\frac{d}{dx}(\frac{x^{2}-x}{x^{3}+x+1})
integral of sqrt(1-64x^2)	\int\:\sqrt{1-64x^{2}}dx
derivative of (xln(x)/(1+ln(x)))	\frac{d}{dx}(\frac{x\ln(x)}{1+\ln(x)})
integral of (x-1)/(x^2-2x)	\int\:\frac{x-1}{x^{2}-2x}dx
d/(dt)(sqrt(2))	\frac{d}{dt}(\sqrt{2})
integral of x+xe^x	\int\:x+xe^{x}dx
area x^3+x^2-6x,6x	area\:x^{3}+x^{2}-6x,6x
area f(x)=x^2-4,[-4,3]	area\:f(x)=x^{2}-4,[-4,3]
integral of cos^4(5x+3)	\int\:\cos^{4}(5x+3)dx
integral of x-5	\int\:x-5dx
derivative of x^3(x-1^2)	\frac{d}{dx}(x^{3}(x-1)^{2})
tangent of y=(3sqrt(x)+x)(2-x^2)	tangent\:y=(3\sqrt{x}+x)(2-x^{2})
derivative of f(x)=(x-7)/(-5x-10)	derivative\:f(x)=\frac{x-7}{-5x-10}
derivative of sqrt(13x^2-5x+8)	\frac{d}{dx}(\sqrt{13x^{2}-5x+8})
7y^'+1y=8e^3x,y(0)=9	7y^{\prime\:}+1y=8e^{3}x,y(0)=9
f(x)=sin(3x)cos(5x)	f(x)=\sin(3x)\cos(5x)
derivative of 1/(sqrt(1+4x))	derivative\:\frac{1}{\sqrt{1+4x}}
d/(dt)((t+pi)/t cos(t))	\frac{d}{dt}(\frac{t+π}{t}\cos(t))
limit as x approaches 0 of 1/(x^2)-1/x	\lim\:_{x\to\:0}(\frac{1}{x^{2}}-\frac{1}{x})
integral of sqrt(2t+1)	\int\:\sqrt{2t+1}dt
integral of sec^6(3x)	\int\:\sec^{6}(3x)dx
y^'-(4y)/t =5	y^{\prime\:}-\frac{4y}{t}=5
derivative of (6x^2+1)/(x^2+9)	derivative\:\frac{6x^{2}+1}{x^{2}+9}
derivative of (-cos(x)/(sqrt(x)))	\frac{d}{dx}(\frac{-\cos(x)}{\sqrt{x}})
integral of (5xe^{2x})/((1+2x)^2)	\int\:\frac{5xe^{2x}}{(1+2x)^{2}}dx
integral of sin^5(3x)cos^3(3x)	\int\:\sin^{5}(3x)\cos^{3}(3x)dx
derivative of arctan(-4x)	\frac{d}{dx}(\arctan(-4x))
derivative of f(x)=(sqrt(x^2+1))/(2x-3)	derivative\:f(x)=\frac{\sqrt{x^{2}+1}}{2x-3}
derivative of (x^2/(1-x))	\frac{d}{dx}(\frac{x^{2}}{1-x})
integral from-1 to 2 of 2\sqrt[3]{5-3x}	\int\:_{-1}^{2}2\sqrt[3]{5-3x}dx
integral of (x^3)/3+x	\int\:\frac{x^{3}}{3}+xdx
integral of cos(3z+4)	\int\:\cos(3z+4)dz
sum from n=1 to infinity of 1/(n2^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n2^{n}}
(dy)/(dx)=12x^{11}y	\frac{dy}{dx}=12x^{11}y
integral of 1/((2+cos(x))^2)	\int\:\frac{1}{(2+\cos(x))^{2}}dx
integral from-1 to 1 of 1.5x^4	\int\:_{-1}^{1}1.5x^{4}dx
integral of (x^2+2)/(x+1)	\int\:\frac{x^{2}+2}{x+1}dx
integral of ((2x))/((sqrt(9-x^4)))	\int\:\frac{(2x)}{(\sqrt{9-x^{4}})}dx
taylor ln(5-2x)	taylor\:\ln(5-2x)
limit as x approaches infinity+of x^{12}	\lim\:_{x\to\:\infty\:+}(x^{12})
d/(dt)(sin(t/2))	\frac{d}{dt}(\sin(\frac{t}{2}))
y^'=5	y^{\prime\:}=5
integral of e^{3/2 x}	\int\:e^{\frac{3}{2}x}dx
t(dy)/(dt)+y=t^2	t\frac{dy}{dt}+y=t^{2}
integral of t/(t^2+1)	\int\:\frac{t}{t^{2}+1}dt
sum from n=1 to infinity of (n+1)x^n	\sum\:_{n=1}^{\infty\:}(n+1)x^{n}
derivative of (ln(x))/(x^2)	derivative\:\frac{\ln(x)}{x^{2}}
limit as x approaches 0+of (2^x)/(3^x)	\lim\:_{x\to\:0+}(\frac{2^{x}}{3^{x}})
integral of ((x+1))/(x^2+2x+8)	\int\:\frac{(x+1)}{x^{2}+2x+8}dx
integral of x^3e^{x^{4+5}}	\int\:x^{3}e^{x^{4+5}}dx
inverse oflaplace 4/(s*(s^2-4s+5))	inverselaplace\:\frac{4}{s\cdot\:(s^{2}-4s+5)}
integral from 0 to 1 of 1/(x^2+2x+1)	\int\:_{0}^{1}\frac{1}{x^{2}+2x+1}dx
derivative of 6x-7e^{6x}	\frac{d}{dx}(6x-7e^{6x})
limit as x approaches 0 of (\|0\|)/0	\lim\:_{x\to\:0}(\frac{\left\|0\right\|}{0})
derivative of 8x^2+3x-2	\frac{d}{dx}(8x^{2}+3x-2)
area x^3-3x^2+2x,0<= x<= 2	area\:x^{3}-3x^{2}+2x,0\le\:x\le\:2
derivative of-3(e^x)^3	derivative\:-3(e^{x})^{3}
area y=x^4-x^2,y=1-x^2	area\:y=x^{4}-x^{2},y=1-x^{2}
y^{''}+y^'-6y=12t+10e^{-3t}	y^{\prime\:\prime\:}+y^{\prime\:}-6y=12t+10e^{-3t}
d/(dθ)(θcos(θ)-sin(θ))	\frac{d}{dθ}(θ\cos(θ)-\sin(θ))
derivative of e^{x+2y}	\frac{d}{dx}(e^{x+2y})

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