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Popular Calculus Problems

derivative of f(x)=2(13-x^4)	derivative\:f(x)=2(13-x^{4})
integral from 1 to 8 of 1/(xsqrt(16x^2-9))	\int\:_{1}^{8}\frac{1}{x\sqrt{16x^{2}-9}}dx
limit as x approaches 6 of cos(1/(x-6))	\lim\:_{x\to\:6}(\cos(\frac{1}{x-6}))
integral of cos(x)sec^3(x)	\int\:\cos(x)\sec^{3}(x)dx
derivative of f(x)=(x^3+3x+2)/(x^2-1)	derivative\:f(x)=\frac{x^{3}+3x+2}{x^{2}-1}
integral from 0 to 2 of integral from 0 to sqrt(2-x^2 of)18xy	\int\:_{0}^{2}\int\:_{0}^{\sqrt{2-x^{2}}}18xydydx
limit as x approaches-2 of (x+2)/(2x+sqrt(x^2+12))	\lim\:_{x\to\:-2}(\frac{x+2}{2x+\sqrt{x^{2}+12}})
limit as x approaches 3 of ((2x^3-5x^2-2x-3))/(4x^3-13x^2+4x-3)	\lim\:_{x\to\:3}(\frac{(2x^{3}-5x^{2}-2x-3)}{4x^{3}-13x^{2}+4x-3})
limit as x approaches 0 of x*cos(x)	\lim\:_{x\to\:0}(x\cdot\:\cos(x))
integral of (-4x+4)/(5(4x^2-4x+5))	\int\:\frac{-4x+4}{5(4x^{2}-4x+5)}dx
f(θ)=4sin(θ)	f(θ)=4\sin(θ)
area y=(14)/x ,y=-64x+72	area\:y=\frac{14}{x},y=-64x+72
(\partial)/(\partial y)(4x^3y^3-3x^2sin(x^3)y)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}-3x^{2}\sin(x^{3})y)
derivative of ((x^2-1^3)/((2x+1)^5))	\frac{d}{dx}(\frac{(x^{2}-1)^{3}}{(2x+1)^{5}})
integral from-2 to 4 of (x^2-2x-8)	\int\:_{-2}^{4}(x^{2}-2x-8)dx
limit as x approaches infinity of (sin(17x))/x	\lim\:_{x\to\:\infty\:}(\frac{\sin(17x)}{x})
(\partial)/(\partial x)(sin(x^2+xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}+xy))
derivative of (xcos(x)/(1+e^x))	\frac{d}{dx}(\frac{x\cos(x)}{1+e^{x}})
(\partial)/(\partial x)(y^5sin(2x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(2x))
area 4-x^2,x^2-2x	area\:4-x^{2},x^{2}-2x
y^{''}-2y^'+y=te^t+4	y^{\prime\:\prime\:}-2y^{\prime\:}+y=te^{t}+4
y^{''}+36y=sec^2(6x)	y^{\prime\:\prime\:}+36y=\sec^{2}(6x)
y^'=3x^2(1+y^2)	y^{\prime\:}=3x^{2}(1+y^{2})
derivative of (x-4/x+ln(x/4))	\frac{d}{dx}(\frac{x-4}{x}+\ln(\frac{x}{4}))
y^{''}-4y^'+3y=0,y(0)=1,y^'(0)= 1/3	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0,y(0)=1,y^{\prime\:}(0)=\frac{1}{3}
derivative of x^4+8x	\frac{d}{dx}(x^{4}+8x)
derivative of f(x)=-4/x	derivative\:f(x)=-\frac{4}{x}
tangent of x^3,\at x=1	tangent\:x^{3},\at\:x=1
derivative of y=(x^6-10)x	derivative\:y=(x^{6}-10)x
(dy)/(dt)=0.0572(400-y),y(0)=32	\frac{dy}{dt}=0.0572(400-y),y(0)=32
y^'+(1-2x)/(x^2)y-1=0	y^{\prime\:}+\frac{1-2x}{x^{2}}y-1=0
(\partial)/(\partial y)(xy+yz+zy)	\frac{\partial\:}{\partial\:y}(xy+yz+zy)
derivative of f(x)=-1/9 (x^{-9}-x^{18})	derivative\:f(x)=-\frac{1}{9}(x^{-9}-x^{18})
integral of 1/(16e^{-5x)+e^{5x}}	\int\:\frac{1}{16e^{-5x}+e^{5x}}dx
tangent of (4-x)y^2=x^3,(2,2)	tangent\:(4-x)y^{2}=x^{3},(2,2)
(\partial)/(\partial y)(-y/(x^2))	\frac{\partial\:}{\partial\:y}(-\frac{y}{x^{2}})
integral of 4x^7	\int\:4x^{7}dx
derivative of f(x)=0.0622x^2+1.1119x+2.3979	derivative\:f(x)=0.0622x^{2}+1.1119x+2.3979
derivative of y=x^5	derivative\:y=x^{5}
integral of (10)/x	\int\:\frac{10}{x}dx
derivative of R(q)=(q^2+1)^4	derivative\:R(q)=(q^{2}+1)^{4}
limit as x approaches 3+of (4x)/(x-3)	\lim\:_{x\to\:3+}(\frac{4x}{x-3})
tangent of y=8(x-1/x)^4,\at x=2	tangent\:y=8(x-\frac{1}{x})^{4},\at\:x=2
derivative of ((x^2-1))/(x-1)	derivative\:\frac{(x^{2}-1)}{x-1}
limit as x approaches 0 of (6e^x-6)/x	\lim\:_{x\to\:0}(\frac{6e^{x}-6}{x})
(dy)/(dx)=((x^2y-y))/((y+1))	\frac{dy}{dx}=\frac{(x^{2}y-y)}{(y+1)}
derivative of cos(4x+sin(4x))	\frac{d}{dx}(\cos(4x)+\sin(4x))
10y^{''}+1000y=0	10y^{\prime\:\prime\:}+1000y=0
(\partial)/(\partial u)(2sin(u)cos(v))	\frac{\partial\:}{\partial\:u}(2\sin(u)\cos(v))
area y=4(x+1),y=5(x+1),x=7	area\:y=4(x+1),y=5(x+1),x=7
limit as x approaches 0 of (sin(x)-cos(x)sin(x))/(x^2)	\lim\:_{x\to\:0}(\frac{\sin(x)-\cos(x)\sin(x)}{x^{2}})
limit as x approaches 0+of (x^2+1)^{1/x}	\lim\:_{x\to\:0+}((x^{2}+1)^{\frac{1}{x}})
limit as x approaches 0+of (sin(x^2))/x	\lim\:_{x\to\:0+}(\frac{\sin(x^{2})}{x})
(dy)/(dx)-2xy=e^{x^2}	\frac{dy}{dx}-2xy=e^{x^{2}}
x((dy)/(dx))+y=y^2	x(\frac{dy}{dx})+y=y^{2}
integral of (3-18x)/(sqrt(64-9x^2))	\int\:\frac{3-18x}{\sqrt{64-9x^{2}}}dx
(dy)/(dx)=(b^2x)/(a^2y)	\frac{dy}{dx}=\frac{b^{2}x}{a^{2}y}
(\partial)/(\partial x)(e^{2x}+yln(x))	\frac{\partial\:}{\partial\:x}(e^{2x}+y\ln(x))
2y^{''}+y^'-10y=0,y(1)=5,y^'(1)=2	2y^{\prime\:\prime\:}+y^{\prime\:}-10y=0,y(1)=5,y^{\prime\:}(1)=2
derivative of (1/(x^2-3/(x^4))(x+5x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{3}{x^{4}})(x+5x^{3}))
3y^'+15y=180	3y^{\prime\:}+15y=180
integral from 0 to 2 of 1/(8+2t^2)	\int\:_{0}^{2}\frac{1}{8+2t^{2}}dt
integral of (arccos(x))	\int\:(\arccos(x))dx
derivative of sqrt(x+x^2)	\frac{d}{dx}(\sqrt{x+x^{2}})
inverse oflaplace 1/(s^2)*3/((s+1))	inverselaplace\:\frac{1}{s^{2}}\cdot\:\frac{3}{(s+1)}
integral of (2x+1)/((x^2+4)^2(x+1)^3)	\int\:\frac{2x+1}{(x^{2}+4)^{2}(x+1)^{3}}dx
derivative of x^7cos(x)	\frac{d}{dx}(x^{7}\cos(x))
derivative of u/(u^2+6)	derivative\:\frac{u}{u^{2}+6}
integral of ((x^2-16)^{3/2})/(x^3)	\int\:\frac{(x^{2}-16)^{\frac{3}{2}}}{x^{3}}dx
integral of 6x^3	\int\:6x^{3}dx
integral of x7^x	\int\:x7^{x}dx
integral of (sin(2x))/(4+cos^2(x))	\int\:\frac{\sin(2x)}{4+\cos^{2}(x)}dx
integral of (x^2+x)e^{1-2x}	\int\:(x^{2}+x)e^{1-2x}dx
integral of sin(9x)cos(6x)	\int\:\sin(9x)\cos(6x)dx
longdivision ((x-1))/(x+1)	longdivision\:\frac{(x-1)}{x+1}
d/(dθ)(cos^2(θ))	\frac{d}{dθ}(\cos^{2}(θ))
y^3-(2x+8)+3xy^2y^'=0	y^{3}-(2x+8)+3xy^{2}y^{\prime\:}=0
(\partial)/(\partial y)(3x^2+4xy+y^2)	\frac{\partial\:}{\partial\:y}(3x^{2}+4xy+y^{2})
(\partial)/(\partial x)(6xy)	\frac{\partial\:}{\partial\:x}(6xy)
y^{''}+y=0,y(pi/3)=0,y^'(pi/3)=4	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=0,y^{\prime\:}(\frac{π}{3})=4
derivative of (tan(1/x)^{sec(1/x)})	\frac{d}{dx}((\tan(\frac{1}{x}))^{\sec(\frac{1}{x})})
integral from 6 to 10 of 1/((x-6)^4)	\int\:_{6}^{10}\frac{1}{(x-6)^{4}}dx
integral of x/(2x+4)	\int\:\frac{x}{2x+4}dx
limit as x approaches 3 of (sqrt(12-x)-3)/(1+x-sqrt(x^2+7))	\lim\:_{x\to\:3}(\frac{\sqrt{12-x}-3}{1+x-\sqrt{x^{2}+7}})
d/(dy)(-2xysin(x^2y))	\frac{d}{dy}(-2xy\sin(x^{2}y))
integral of 1/(sin^2(θ))	\int\:\frac{1}{\sin^{2}(θ)}dθ
integral of 1/(sqrt(12x+0.02x^2))	\int\:\frac{1}{\sqrt{12x+0.02x^{2}}}dx
derivative of sin(ln((x^2+4^4)))	\frac{d}{dx}(\sin(\ln((x^{2}+4)^{4})))
7x-8ysqrt(x^2+1)(dy)/(dx)=0	7x-8y\sqrt{x^{2}+1}\frac{dy}{dx}=0
integral of (2x+2)/(x^2-2x+1)	\int\:\frac{2x+2}{x^{2}-2x+1}dx
limit as x approaches 8 of (x^2-5)/(x-8)	\lim\:_{x\to\:8}(\frac{x^{2}-5}{x-8})
integral of x(3x^2+1)	\int\:x(3x^{2}+1)dx
(dy}{dx}=\frac{e^{sqrt(x)})/y	\frac{dy}{dx}=\frac{e^{\sqrt{x}}}{y}
integral of-picos(pix)	\int\:-π\cos(πx)dx
integral of 1/(sqrt((4x)^2+2^2))	\int\:\frac{1}{\sqrt{(4x)^{2}+2^{2}}}dx
(dy)/(dt)+2/t y=4t-3+2/t	\frac{dy}{dt}+\frac{2}{t}y=4t-3+\frac{2}{t}
limit as x approaches 10 of (sqrt(x-1)-3)/(x-10)	\lim\:_{x\to\:10}(\frac{\sqrt{x-1}-3}{x-10})
derivative of sqrt(7)u+sqrt(2u)	derivative\:\sqrt{7}u+\sqrt{2u}
sum from n=0 to infinity of (sin(100))^n	\sum\:_{n=0}^{\infty\:}(\sin(100))^{n}
integral of x/(sqrt(x))	\int\:\frac{x}{\sqrt{x}}dx

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