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Popular Calculus Problems

(d^2y)/(dt^2)+2(dy)/(dt)+2y=cos(2t)	\frac{d^{2}y}{dt^{2}}+2\frac{dy}{dt}+2y=\cos(2t)
derivative of 7e	derivative\:7e
x*(dy)/(dx)=7xe^x-y+9x^2	x\cdot\:\frac{dy}{dx}=7xe^{x}-y+9x^{2}
integral of e^{3θ}sin(2θ)	\int\:e^{3θ}\sin(2θ)dθ
integral of sqrt(1+4θ^2)	\int\:\sqrt{1+4θ^{2}}dθ
laplacetransform e^{2t}(t-1)^2	laplacetransform\:e^{2t}(t-1)^{2}
derivative of (1-3xarccoth(3x))	\frac{d}{dx}((1-3x)\arccoth(3x))
y^'+4xy^3=0	y^{\prime\:}+4xy^{3}=0
derivative of (4x^3/3+cos(x)+1)	\frac{d}{dx}(\frac{4x^{3}}{3}+\cos(x)+1)
derivative of sin(nx)	\frac{d}{dx}(\sin(nx))
(\partial)/(\partial y)(ln(yz))	\frac{\partial\:}{\partial\:y}(\ln(yz))
integral of 1/(x-y)	\int\:\frac{1}{x-y}dx
integral from-1 to 1 of (13-12u)^{-1}	\int\:_{-1}^{1}(13-12u)^{-1}du
limit as x approaches-3 of 4	\lim\:_{x\to\:-3}(4)
(\partial)/(\partial x)(x^4+3^y+x^y)	\frac{\partial\:}{\partial\:x}(x^{4}+3^{y}+x^{y})
limit as h approaches 0 of 3x^2-2xh+5h	\lim\:_{h\to\:0}(3x^{2}-2xh+5h)
tangent of 2e^xcos(x)(0.2)	tangent\:2e^{x}\cos(x)(0.2)
integral of sqrt(11-x^2)	\int\:\sqrt{11-x^{2}}dx
(\partial)/(\partial x)(3cos(x))	\frac{\partial\:}{\partial\:x}(3\cos(x))
derivative of f(t)=4sec(9)(pit-2)	derivative\:f(t)=4\sec(9)(πt-2)
integral of cos^4(2pix)	\int\:\cos^{4}(2πx)dx
integral of sin(nx)sin(mx)	\int\:\sin(nx)\sin(mx)dx
tangent of f(x)= 3/(2sqrt(3x+1)),\at x=8	tangent\:f(x)=\frac{3}{2\sqrt{3x+1}},\at\:x=8
y^'= y/x+x/(2(y+x))	y^{\prime\:}=\frac{y}{x}+\frac{x}{2(y+x)}
integral from 2 to 5 of x/(sqrt(x-1))	\int\:_{2}^{5}\frac{x}{\sqrt{x-1}}dx
derivative of 1/(4x^2+1)	\frac{d}{dx}(\frac{1}{4x^{2}+1})
(\partial)/(\partial x)(((2x+3y))/(4x+5y))	\frac{\partial\:}{\partial\:x}(\frac{(2x+3y)}{4x+5y})
f(x)=sqrt(x^2+5)	f(x)=\sqrt{x^{2}+5}
taylor cos(pix),1	taylor\:\cos(πx),1
integral from 0 to 1 of (x^4+1)/x	\int\:_{0}^{1}\frac{x^{4}+1}{x}dx
integral of sqrt(1+sinh^2(x))	\int\:\sqrt{1+\sinh^{2}(x)}dx
integral of 3cos(x)-4sin(x)	\int\:3\cos(x)-4\sin(x)dx
derivative of 6e^{6x}	derivative\:6e^{6x}
area y=5-x^2,y=x^2-3	area\:y=5-x^{2},y=x^{2}-3
integral of 1/(xsqrt(16-x^2))	\int\:\frac{1}{x\sqrt{16-x^{2}}}dx
derivative of f^9	derivative\:f^{9}
integral of (7x^3)/(sqrt(4+x^2))	\int\:\frac{7x^{3}}{\sqrt{4+x^{2}}}dx
tangent of y=-2x^3,(1,-2)	tangent\:y=-2x^{3},(1,-2)
integral of (3x^2)	\int\:(3x^{2})dx
(\partial)/(\partial x)(sin^2(3xy^2-y))	\frac{\partial\:}{\partial\:x}(\sin^{2}(3xy^{2}-y))
implicit (dy)/(dx),y=11^x	implicit\:\frac{dy}{dx},y=11^{x}
derivative of (x^2-3e^x)	\frac{d}{dx}((x^{2}-3)e^{x})
integral of (3x^2+1)/(x^5-x)	\int\:\frac{3x^{2}+1}{x^{5}-x}dx
slope ofintercept (0.5)(-2.4)	slopeintercept\:(0.5)(-2.4)
y^'=5y+y^6,y(0)=1	y^{\prime\:}=5y+y^{6},y(0)=1
integral from 0 to x of 1/(t^2+t+1)	\int\:_{0}^{x}\frac{1}{t^{2}+t+1}dt
limit as x approaches 0 of sec(2x)	\lim\:_{x\to\:0}(\sec(2x))
inverse oflaplace 1/(s-4)	inverselaplace\:\frac{1}{s-4}
integral of ((7-4x^3+6x^6))/(x^6)	\int\:\frac{(7-4x^{3}+6x^{6})}{x^{6}}dx
derivative of x^5(2x-1^7)	\frac{d}{dx}(x^{5}(2x-1)^{7})
derivative of (x+7/(x^3+x-6))	\frac{d}{dx}(\frac{x+7}{x^{3}+x-6})
limit as x approaches 1 of \|-x^2+1\|	\lim\:_{x\to\:1}(\left\|-x^{2}+1\right\|)
x*(dy)/(dx)+7y= 1/x	x\cdot\:\frac{dy}{dx}+7y=\frac{1}{x}
integral of e^{5x}sin(5x)	\int\:e^{5x}\sin(5x)dx
area y=cos(x),x= pi/4 ,x= pi/3	area\:y=\cos(x),x=\frac{π}{4},x=\frac{π}{3}
(dy)/(dx)+y=0	\frac{dy}{dx}+y=0
integral of 1/(sqrt(x)(1+x))	\int\:\frac{1}{\sqrt{x}(1+x)}dx
(\partial)/(\partial x)(2^x)	\frac{\partial\:}{\partial\:x}(2^{x})
integral from-3 to 3 of 1/(x^2+9)	\int\:_{-3}^{3}\frac{1}{x^{2}+9}dx
derivative of 10cos(t)	derivative\:10\cos(t)
derivative of (3x-1^4(7x^2-4)^{-3})	\frac{d}{dx}((3x-1)^{4}(7x^{2}-4)^{-3})
integral of 4x(3x-1)^5	\int\:4x(3x-1)^{5}dx
tangent of x^2+2xy-y^2+x=20,(3,4)	tangent\:x^{2}+2xy-y^{2}+x=20,(3,4)
tangent of (3x+6)^{1/5},\at x=2	tangent\:(3x+6)^{\frac{1}{5}},\at\:x=2
(\partial)/(\partial x)(x^2y^2e^{4xy})	\frac{\partial\:}{\partial\:x}(x^{2}y^{2}e^{4xy})
derivative of (x*sinh(x+cos(x))^5)	\frac{d}{dx}((x\cdot\:\sinh(x)+\cos(x))^{5})
derivative of (x+6/(x^3+x-8))	\frac{d}{dx}(\frac{x+6}{x^{3}+x-8})
derivative of x^2-2x-1	derivative\:x^{2}-2x-1
inverse oflaplace ((s+4))/(s^2+4s+29)	inverselaplace\:\frac{(s+4)}{s^{2}+4s+29}
integral of 1	\int\:1
derivative of 4sec^2(x)-6sec^4(x)	derivative\:4\sec^{2}(x)-6\sec^{4}(x)
y^{''}+1y=xe^{5x}	y^{\prime\:\prime\:}+1y=xe^{5x}
(\partial)/(\partial x)(x^2sin(xy+z))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(xy+z))
2xy^'-2xy=-e^{-2x}y^3	2xy^{\prime\:}-2xy=-e^{-2x}y^{3}
derivative of (x+2)(x-5)(x-1)	derivative\:(x+2)(x-5)(x-1)
limit as x approaches 0 of 3(h+2x)2	\lim\:_{x\to\:0}(3(h+2x)2)
integral of 5/(x+2)	\int\:\frac{5}{x+2}dx
derivative of 4x^2(3x-1^3)	\frac{d}{dx}(4x^{2}(3x-1)^{3})
tangent of y=7x^2-x^3,(1,6)	tangent\:y=7x^{2}-x^{3},(1,6)
integral of e^{xz}	\int\:e^{xz}dy
derivative of (x^2-2^3)	\frac{d}{dx}((x^{2}-2)^{3})
integral of 5x^{-1}	\int\:5x^{-1}dx
derivative of sqrt(r)+\sqrt[8]{r}	derivative\:\sqrt{r}+\sqrt[8]{r}
derivative of (1+x/(x^3))	\frac{d}{dx}(\frac{1+x}{x^{3}})
(\partial)/(\partial x)(sqrt(xye^y))	\frac{\partial\:}{\partial\:x}(\sqrt{xye^{y}})
y^'+7y=e^{6x}	y^{\prime\:}+7y=e^{6x}
integral from 0 to 2pi of sin^2(x)	\int\:_{0}^{2π}\sin^{2}(x)dx
sum from n=1 to infinity of n^{-1/5}	\sum\:_{n=1}^{\infty\:}n^{-\frac{1}{5}}
limit as x approaches 2-of (5x)/(x-6)	\lim\:_{x\to\:2-}(\frac{5x}{x-6})
derivative of f(x)=(x^3+2)e^x	derivative\:f(x)=(x^{3}+2)e^{x}
limit as x approaches-2 of x^2-4x+6	\lim\:_{x\to\:-2}(x^{2}-4x+6)
derivative of ln(2x-5)	derivative\:\ln(2x-5)
inverse oflaplace arctan(s)	inverselaplace\:\arctan(s)
integral of e^{-x}x^2	\int\:e^{-x}x^{2}dx
derivative of 3ab^2x^4	\frac{d}{dx}(3ab^{2}x^{4})
integral of 6sin(2x)-3cos(3x)	\int\:6\cdot\:\sin(2x)-3\cdot\:\cos(3x)dx
x(dy)/(dx)=y	x\frac{dy}{dx}=y
xdy=y+x(cos(y/x))^2dx	xdy=y+x(\cos(\frac{y}{x}))^{2}dx
derivative of 2x^3+3x^2-12x+1	derivative\:2x^{3}+3x^{2}-12x+1
limit as x approaches 0+of x-1/x+3	\lim\:_{x\to\:0+}(x-\frac{1}{x}+3)

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