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Popular Calculus Problems

inverse oflaplace (2s+3)/(s^2+6s+13)	inverselaplace\:\frac{2s+3}{s^{2}+6s+13}
1/5 (dy)/(dx)=(1/5)^2-1/5	\frac{1}{5}\frac{dy}{dx}=(\frac{1}{5})^{2}-\frac{1}{5}
inverse oflaplace (5x+5)/(x^2-4)	inverselaplace\:\frac{5x+5}{x^{2}-4}
(\partial)/(\partial x)(12xy^2)	\frac{\partial\:}{\partial\:x}(12xy^{2})
integral from 0 to 1 of ((x^2+1)e^{-x})	\int\:_{0}^{1}((x^{2}+1)e^{-x})dx
derivative of (x^2-1(-3x^3+2x))	\frac{d}{dx}((x^{2}-1)(-3x^{3}+2x))
(\partial)/(\partial x)(2x-2y)	\frac{\partial\:}{\partial\:x}(2x-2y)
limit as x approaches-1 of h(x)	\lim\:_{x\to\:-1}(h(x))
tangent of f(x)= 8/(7-x)	tangent\:f(x)=\frac{8}{7-x}
inverse oflaplace {1/(s^2)-(48)/(s^5)}	inverselaplace\:\left\{\frac{1}{s^{2}}-\frac{48}{s^{5}}\right\}
d/(dθ)(3cos(θ)-4sin(θ))	\frac{d}{dθ}(3\cos(θ)-4\sin(θ))
area y=x^4,x=y^7,x=0,x=1	area\:y=x^{4},x=y^{7},x=0,x=1
integral from 0 to 1 of arctan(x)	\int\:_{0}^{1}\arctan(x)dx
(\partial)/(\partial x)((x-2)^2+(y-2)^2)	\frac{\partial\:}{\partial\:x}((x-2)^{2}+(y-2)^{2})
(\partial)/(\partial s)(r+s)	\frac{\partial\:}{\partial\:s}(r+s)
integral of (tan(x))/(sec(x))	\int\:\frac{\tan(x)}{\sec(x)}dx
integral of (2x)/(x^2+1)	\int\:\frac{2x}{x^{2}+1}dx
integral of x/(2x+3)	\int\:\frac{x}{2x+3}dx
derivative of f(x)= x/(7x^2+1)	derivative\:f(x)=\frac{x}{7x^{2}+1}
(dy)/(dt)=-1/5 y	\frac{dy}{dt}=-\frac{1}{5}y
integral from pi to 5pi of x^2sin(x)	\int\:_{π}^{5π}x^{2}\sin(x)dx
taylor 3+4x^2-5x^3	taylor\:3+4x^{2}-5x^{3}
integral of 1/(1+x/2)	\int\:\frac{1}{1+\frac{x}{2}}dx
sum from n=1 to infinity of (3^n)/(4^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{4^{n+1}}
limit as x approaches 1 of 4sqrt(x-1)	\lim\:_{x\to\:1}(4\sqrt{x-1})
derivative of (150000)/((4t+75)^2)	derivative\:\frac{150000}{(4t+75)^{2}}
derivative of g(x)= 3/(x^3)	derivative\:g(x)=\frac{3}{x^{3}}
integral of 1/(xsqrt(1+ln(x^2)))	\int\:\frac{1}{x\sqrt{1+\ln(x^{2})}}dx
(\partial)/(\partial x)(sqrt(25-x^2-5y))	\frac{\partial\:}{\partial\:x}(\sqrt{25-x^{2}-5y})
sum from n=0 to infinity of 5/(pi^n)	\sum\:_{n=0}^{\infty\:}\frac{5}{π^{n}}
derivative of 4+2x-3x^2-5x^3-8x^4+9x^5	\frac{d}{dx}(4+2x-3x^{2}-5x^{3}-8x^{4}+9x^{5})
integral from 0 to 2pi of sqrt(20+16t^2)	\int\:_{0}^{2π}\sqrt{20+16t^{2}}dt
limit as x approaches-2 of (x+1)^4(2x^2)	\lim\:_{x\to\:-2}((x+1)^{4}(2x^{2}))
derivative of (x^2+9)/(x+3)	derivative\:\frac{x^{2}+9}{x+3}
integral from 0 to 2 of 1/(sqrt(4+x^2))	\int\:_{0}^{2}\frac{1}{\sqrt{4+x^{2}}}dx
tangent of f(x)= 2/(x+1),\at x=1	tangent\:f(x)=\frac{2}{x+1},\at\:x=1
xy^'-2y=11x^2	xy^{\prime\:}-2y=11x^{2}
derivative of 2^{e^x}	\frac{d}{dx}(2^{e^{x}})
(dy)/(dx)=(-2y)/(x-2)	\frac{dy}{dx}=\frac{-2y}{x-2}
(\partial)/(\partial x)(sqrt(3x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{3x^{2}+y^{2}})
integral from-1 to 1 of 3x^2sqrt(x^3+2)	\int\:_{-1}^{1}3x^{2}\sqrt{x^{3}+2}dx
limit as x approaches-1 of t^2-x^2	\lim\:_{x\to\:-1}(t^{2}-x^{2})
integral of ((x^2-3x-7))/((2x+3)(x+1)^2)	\int\:\frac{(x^{2}-3x-7)}{(2x+3)(x+1)^{2}}dx
derivative of 3x^4-6x^3+1	derivative\:3x^{4}-6x^{3}+1
derivative of f(x)=(x^2+8)/(9x-2)	derivative\:f(x)=\frac{x^{2}+8}{9x-2}
derivative of x^{10}e^x	derivative\:x^{10}e^{x}
derivative of e^{x/2}	derivative\:e^{\frac{x}{2}}
derivative of ux	\frac{d}{dx}(ux)
integral from 0 to 9 of \|sqrt(5x+6)-x\|	\int\:_{0}^{9}\left\|\sqrt{5x+6}-x\right\|dx
slope of (0,3),(1,0)	slope\:(0,3),(1,0)
integral of (x^2)/((x-6)(x-7)^2)	\int\:\frac{x^{2}}{(x-6)(x-7)^{2}}dx
laplacetransform te^{7t}	laplacetransform\:te^{7t}
(dy)/(dt)=3y+y^5,y(0)=1	\frac{dy}{dt}=3y+y^{5},y(0)=1
integral of xsec(3x^2+1)	\int\:x\sec(3x^{2}+1)dx
6(dy)/(dx)-2y=xy^4,y(0)=-2	6\frac{dy}{dx}-2y=xy^{4},y(0)=-2
((2y)/x+2x)+(2ln(x)-3)((dy)/(dx))=0	(\frac{2y}{x}+2x)+(2\ln(x)-3)(\frac{dy}{dx})=0
derivative of 1/(4^x)	derivative\:\frac{1}{4^{x}}
integral from 1/2 to 1 of 4/9 x(5-x^2)	\int\:_{\frac{1}{2}}^{1}\frac{4}{9}x(5-x^{2})dx
derivative of (t-sqrt(t))/(t^{1/7)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{7}}}
d/(d{x)}({x}sin({y}-{z}))	\frac{d}{d{x}}({x}\sin({y}-{z}))
derivative of y=((3x^2)/(2x+4))^3	derivative\:y=(\frac{3x^{2}}{2x+4})^{3}
inverse oflaplace 5/(s(s^2+5^2))	inverselaplace\:\frac{5}{s(s^{2}+5^{2})}
laplacetransform f(t)=2(1-e^{-5t})	laplacetransform\:f(t)=2(1-e^{-5t})
derivative of ln^2(2*2^x)	\frac{d}{dx}(\ln^{2}(2)\cdot\:2^{x})
derivative of y=ln(x-4)	derivative\:y=\ln(x-4)
laplacetransform-5e^{2t}	laplacetransform\:-5e^{2t}
sum from n=1 to infinity of n!(x-1)^n	\sum\:_{n=1}^{\infty\:}n!(x-1)^{n}
integral from 1 to 4 of x^2-3x	\int\:_{1}^{4}x^{2}-3xdx
integral from 0 to 4 of x/(x^2-1)	\int\:_{0}^{4}\frac{x}{x^{2}-1}dx
(\partial)/(\partial x)(sqrt(3x+2y-3))	\frac{\partial\:}{\partial\:x}(\sqrt{3x+2y-3})
area y=x^2,y=3-x,(0,1.3)	area\:y=x^{2},y=3-x,(0,1.3)
derivative of f(x)=3x^2e^x+e^x(x^3+1)	derivative\:f(x)=3x^{2}e^{x}+e^{x}(x^{3}+1)
y^'=18.2-0.7y	y^{\prime\:}=18.2-0.7y
limit as x approaches 4 of x	\lim\:_{x\to\:4}(x)
inverse oflaplace (s+3)/((s+3)^2+4)	inverselaplace\:\frac{s+3}{(s+3)^{2}+4}
derivative of 1/2 cos(x/2)	\frac{d}{dx}(\frac{1}{2}\cos(\frac{x}{2}))
y^'=y^2+y	y^{\prime\:}=y^{2}+y
derivative of (3x+2^6)	\frac{d}{dx}((3x+2)^{6})
integral from-7 to 7 of 1/x	\int\:_{-7}^{7}\frac{1}{x}dx
tangent of y= x/(sqrt(9+x^2)),(0,0)	tangent\:y=\frac{x}{\sqrt{9+x^{2}}},(0,0)
integral of sqrt(3+x)*(x+1)^2	\int\:\sqrt{3+x}\cdot\:(x+1)^{2}dx
(\partial)/(\partial x)(x^{1/2})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}})
derivative of (-8x/(x^2+1))	\frac{d}{dx}(\frac{-8x}{x^{2}+1})
area y=3x^2ln(x),y=12ln(x)	area\:y=3x^{2}\ln(x),y=12\ln(x)
integral of (x^2+y^2)	\int\:(x^{2}+y^{2})dx
integral of sqrt(4)-x^2	\int\:\sqrt{4}-x^{2}dx
integral of xe^{11x}	\int\:xe^{11x}dx
area 3cos(pix),12x^2-3,-0.5,0.5	area\:3\cos(πx),12x^{2}-3,-0.5,0.5
integral of (x^2-y^2)/((x^2+y^2)^2)	\int\:\frac{x^{2}-y^{2}}{(x^{2}+y^{2})^{2}}dy
derivative of e^{xy^2}	derivative\:e^{xy^{2}}
integral of 1/(3^{2x)}	\int\:\frac{1}{3^{2x}}dx
derivative of-1/(2x^{3/2})	\frac{d}{dx}(-\frac{1}{2x^{\frac{3}{2}}})
limit as x approaches 0 of tan^x(2x)	\lim\:_{x\to\:0}(\tan^{x}(2x))
derivative of y=2x^2sqrt(25-x^2)	derivative\:y=2x^{2}\sqrt{25-x^{2}}
y^'=xy-y	y^{\prime\:}=xy-y
integral of (2x)/(x^2+2)	\int\:\frac{2x}{x^{2}+2}dx
2y^{''}+5y^'-3y=0,y(0)=3,y^'(0)=19	2y^{\prime\:\prime\:}+5y^{\prime\:}-3y=0,y(0)=3,y^{\prime\:}(0)=19
derivative of f(x)= 7/(8t^4)	derivative\:f(x)=\frac{7}{8t^{4}}
tangent of f(x)=2x^3-x^2+2,\at x=1	tangent\:f(x)=2x^{3}-x^{2}+2,\at\:x=1
derivative of ln(2-3x)	\frac{d}{dx}(\ln(2-3x))

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