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Popular Calculus Problems

integral of ((x^3+64))/(x^2+64)	\int\:\frac{(x^{3}+64)}{x^{2}+64}dx
inverse oflaplace 1/(s(s^2+34.5s+1000))	inverselaplace\:\frac{1}{s(s^{2}+34.5s+1000)}
integral from 0 to 7 of 1	\int\:_{0}^{7}1
limit as x approaches 5 of x^2-2x-15	\lim\:_{x\to\:5}(x^{2}-2x-15)
derivative of (x(x^2+4))^{1/3}	derivative\:(x(x^{2}+4))^{\frac{1}{3}}
(\partial)/(\partial x)(sqrt(6+3x^2-2y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{6+3x^{2}-2y^{2}})
integral of 4x^2+1/((2x)^2)	\int\:4x^{2}+\frac{1}{(2x)^{2}}dx
laplacetransform 2t^4	laplacetransform\:2t^{4}
x(dy)/(dx)=y+2xe^{-y/x}	x\frac{dy}{dx}=y+2xe^{-\frac{y}{x}}
inverse oflaplace (6s)/((s^2-8s+25))	inverselaplace\:\frac{6s}{(s^{2}-8s+25)}
integral of 6/(xln(7x))	\int\:\frac{6}{x\ln(7x)}dx
(dy)/(dx)=x-2.5y	\frac{dy}{dx}=x-2.5y
maclaurin 1.5(1+e^{-0.2t})	maclaurin\:1.5(1+e^{-0.2t})
limit as x approaches 0 of (1-4x)^{6/x}	\lim\:_{x\to\:0}((1-4x)^{\frac{6}{x}})
f(x)=2cos(3x)+3e^{-0.25x}	f(x)=2\cos(3x)+3e^{-0.25x}
limit as (x,y) approaches (0,0) of 0	\lim\:_{(x,y)\to\:(0,0)}(0)
derivative of-(x^2/4)	\frac{d}{dx}(-\frac{x^{2}}{4})
integral of zcos(yz)	\int\:z\cos(yz)dy
integral from-1 to 1 of x^7(1+x^8)^7	\int\:_{-1}^{1}x^{7}(1+x^{8})^{7}dx
derivative of f(x)=(13-x^4)/3	derivative\:f(x)=\frac{13-x^{4}}{3}
integral of sec^2(x)+6	\int\:\sec^{2}(x)+6dx
inverse oflaplace ((e^{-4s}))/((s+2)^3)	inverselaplace\:\frac{(e^{-4s})}{(s+2)^{3}}
(\partial)/(\partial x)((x-3)^2+(y-2)^2)	\frac{\partial\:}{\partial\:x}((x-3)^{2}+(y-2)^{2})
inverse oflaplace {1/(s^4-9)}	inverselaplace\:\left\{\frac{1}{s^{4}-9}\right\}
derivative of y=9e^x+4/(\sqrt[3]{x)}	derivative\:y=9e^{x}+\frac{4}{\sqrt[3]{x}}
derivative of sqrt(-5t+3)+t^7	derivative\:\sqrt{-5t+3}+t^{7}
integral from-2 to 2 of t^3(3+t^4)^3	\int\:_{-2}^{2}t^{3}(3+t^{4})^{3}dt
limit as h approaches+0 of h/(sin(3h))	\lim\:_{h\to\:+0}(\frac{h}{\sin(3h)})
integral of (0.3y^4-8y^{-3}+2)	\int\:(0.3y^{4}-8y^{-3}+2)dy
limit as x approaches-1+of x	\lim\:_{x\to\:-1+}(x)
derivative of ((1+x^2+x^4)/(1+x+x^2))	\frac{d}{dx}(\frac{(1+x^{2}+x^{4})}{1+x+x^{2}})
y^'-9/x y=(y^5)/(x^{20)}	y^{\prime\:}-\frac{9}{x}y=\frac{y^{5}}{x^{20}}
y^{''}+16y=sin(4t)	y^{\prime\:\prime\:}+16y=\sin(4t)
limit as x approaches 0+of 2/(x^2)	\lim\:_{x\to\:0+}(\frac{2}{x^{2}})
integral of 1/(sqrt(x^2+2x+10))	\int\:\frac{1}{\sqrt{x^{2}+2x+10}}dx
derivative of (x+1*e^{arctan(x)})	\frac{d}{dx}((x+1)\cdot\:e^{\arctan(x)})
derivative of-e^{-x^2}	\frac{d}{dx}(-e^{-x^{2}})
(dy)/(dt)=3y+y^4	\frac{dy}{dt}=3y+y^{4}
integral of 4x+5	\int\:4x+5dx
((sqrt(3))/3)^'	(\frac{\sqrt{3}}{3})^{\prime\:}
derivative of cos(xcos(2x)cos(4x)sin(x))	\frac{d}{dx}(\cos(x)\cos(2x)\cos(4x)\sin(x))
integral of (2r)/(sqrt(4-r^2))	\int\:\frac{2r}{\sqrt{4-r^{2}}}dr
derivative of f(x)=(2x^2-7)^5-(1+4x^3)^5	derivative\:f(x)=(2x^{2}-7)^{5}-(1+4x^{3})^{5}
(\partial)/(\partial x)(3cos(x)-sin(x)y)	\frac{\partial\:}{\partial\:x}(3\cos(x)-\sin(x)y)
integral from 1 to 3 of 5/(x^2)	\int\:_{1}^{3}\frac{5}{x^{2}}dx
derivative of cos(arcsin(4x))	\frac{d}{dx}(\cos(\arcsin(4x)))
derivative of 14x^6-5x^4+15x^2-8	\frac{d}{dx}(14x^{6}-5x^{4}+15x^{2}-8)
derivative of f(x)=xe^{3x^2}+1	derivative\:f(x)=xe^{3x^{2}}+1
tangent of 4/(x^5)-1/(x^2)	tangent\:\frac{4}{x^{5}}-\frac{1}{x^{2}}
integral of (cos(x))/(1+8sin(x))	\int\:\frac{\cos(x)}{1+8\sin(x)}dx
(dy)/(dx)=(x/y)	\frac{dy}{dx}=(\frac{x}{y})
taylor 4/x ,1	taylor\:\frac{4}{x},1
derivative of (3x^2+3(2x^2+1))	\frac{d}{dx}((3x^{2}+3)(2x^{2}+1))
derivative of 2x^2-2x+4	derivative\:2x^{2}-2x+4
y^{'''}-9y^{''}+18y^'=e^{e^{-3x}}	y^{\prime\:\prime\:\prime\:}-9y^{\prime\:\prime\:}+18y^{\prime\:}=e^{e^{-3x}}
(\partial)/(\partial t)(r/t)	\frac{\partial\:}{\partial\:t}(\frac{r}{t})
derivative of ((mv^2))/r	derivative\:\frac{(mv^{2})}{r}
(dy)/(dx)=xy+2x	\frac{dy}{dx}=xy+2x
integral of-(20)/(x^{21)}	\int\:-\frac{20}{x^{21}}dx
derivative of e^xsin^2(x)	\frac{d}{dx}(e^{x}\sin^{2}(x))
integral of 4/175 x^3	\int\:\frac{4}{175}x^{3}dx
derivative of cos(tan(7x))	\frac{d}{dx}(\cos(\tan(7x)))
derivative of xsqrt(3+x^2)	\frac{d}{dx}(x\sqrt{3+x^{2}})
derivative of tan(x)-sin(x)	derivative\:\tan(x)-\sin(x)
(\partial)/(\partial x)(ln(x+8y+7z))	\frac{\partial\:}{\partial\:x}(\ln(x+8y+7z))
integral of (1/(t^2)+sqrt(t))	\int\:(\frac{1}{t^{2}}+\sqrt{t})dt
integral of (7/x-3/(x^2))	\int\:(\frac{7}{x}-\frac{3}{x^{2}})dx
integral of (3x^5-8)^96x^4	\int\:(3x^{5}-8)^{9}6x^{4}dx
y^'=(xy^3)/((1+x^2)^{1/2)}	y^{\prime\:}=\frac{xy^{3}}{(1+x^{2})^{\frac{1}{2}}}
derivative of arctan(a/x)	\frac{d}{dx}(\arctan(\frac{a}{x}))
integral of 1/(1+sin(x)+cos(x))	\int\:\frac{1}{1+\sin(x)+\cos(x)}dx
f(x)= 1/(3x+2)	f(x)=\frac{1}{3x+2}
integral of (9x^2-36x)/4+18	\int\:\frac{9x^{2}-36x}{4}+18dx
(dy)/(dx)=cos(x+y)	\frac{dy}{dx}=\cos(x+y)
(\partial)/(\partial y)(cos(x)-y)	\frac{\partial\:}{\partial\:y}(\cos(x)-y)
integral of (x^4+1)/(x^4-1)	\int\:\frac{x^{4}+1}{x^{4}-1}dx
integral of (2x-1)/((x-1)(x-2)(2x-3))	\int\:\frac{2x-1}{(x-1)(x-2)(2x-3)}dx
integral of (1+x)/(x^2+2x-1)	\int\:\frac{1+x}{x^{2}+2x-1}dx
derivative of e^{-x}cos(y)	\frac{d}{dx}(e^{-x}\cos(y))
derivative of (1+x^3^5)	\frac{d}{dx}((1+x^{3})^{5})
(\partial)/(\partial y)(e^ysin(x)y)	\frac{\partial\:}{\partial\:y}(e^{y}\sin(x)y)
integral of (x^2sin(x)-2x+3)/(x^2)	\int\:\frac{x^{2}\sin(x)-2x+3}{x^{2}}dx
(dy)/(dt)=-6/((2000+6t))	\frac{dy}{dt}=-\frac{6}{(2000+6t)}
integral of (e^x)/(e^{2x)-1}	\int\:\frac{e^{x}}{e^{2x}-1}dx
derivative of (1/2)^x-x	derivative\:(\frac{1}{2})^{x}-x
integral from-1 to 1 of 3/4 x^2(1-x^2)	\int\:_{-1}^{1}\frac{3}{4}x^{2}(1-x^{2})dx
integral of-5tan^3(x)	\int\:-5\tan^{3}(x)dx
simplify f(3)	simplify\:f(3)
y^{''}+y=9e^{-4x},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y=9e^{-4x},y(0)=0,y^{\prime\:}(0)=0
derivative of ce^{-2x^2}	\frac{d}{dx}(ce^{-2x^{2}})
derivative of sin(xos(x))	\frac{d}{dx}(\sin(x)os(x))
integral of csc(3x)	\int\:\csc(3x)dx
y^'=y-y^2,y(0)=9	y^{\prime\:}=y-y^{2},y(0)=9
inverse oflaplace 2/((s+2)(s+3)^2)	inverselaplace\:\frac{2}{(s+2)(s+3)^{2}}
integral of 5xe^x	\int\:5xe^{x}dx
integral from pi/6 to pi/4 of tan(x)	\int\:_{\frac{π}{6}}^{\frac{π}{4}}\tan(x)dx
inverse oflaplace 1/(s^4(s^2-4))	inverselaplace\:\frac{1}{s^{4}(s^{2}-4)}
area y^2-4x=4,4x-y=16	area\:y^{2}-4x=4,4x-y=16
limit as x approaches 1 of 7-2x-x^2	\lim\:_{x\to\:1}(7-2x-x^{2})
derivative of ((-sin(x)/(1-cos(x)))^2)	\frac{d}{dx}((\frac{-\sin(x)}{1-\cos(x)})^{2})

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