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Popular Calculus Problems

integral of (2x+5)e^x	\int\:(2x+5)e^{x}dx
y^'-2xy=e^{x^2}	y^{\prime\:}-2xy=e^{x^{2}}
integral of (2x^{10}+4x^9+x^8+10)	\int\:(2x^{10}+4x^{9}+x^{8}+10)dx
integral of x^2(x^2-6x+9)	\int\:x^{2}(x^{2}-6x+9)dx
derivative of 10x^2-5x+9	\frac{d}{dx}(10x^{2}-5x+9)
integral of (e^x+1)^3	\int\:(e^{x}+1)^{3}dx
integral of (3x^2-6x+9/x+4e^x)	\int\:(3x^{2}-6x+\frac{9}{x}+4e^{x})dx
y^'=0.05y-12*4000	y^{\prime\:}=0.05y-12\cdot\:4000
derivative of xsin(x+y+ycos(x))	\frac{d}{dx}(x\sin(x+y)+y\cos(x))
d/(dt)(t/(1+t^2))	\frac{d}{dt}(\frac{t}{1+t^{2}})
area x^2,1,0	area\:x^{2},1,0
tangent of f(x)=9x^2+7x-6	tangent\:f(x)=9x^{2}+7x-6
(\partial)/(\partial x)(-3xy^2-2ycos(x))	\frac{\partial\:}{\partial\:x}(-3xy^{2}-2y\cos(x))
integral of 1/(t^2sqrt(169-t^2))	\int\:\frac{1}{t^{2}\sqrt{169-t^{2}}}dt
normal of y=(sqrt(x))/(x+6),(4,0.2)	normal\:y=\frac{\sqrt{x}}{x+6},(4,0.2)
integral from 1 to e of ln(12x)	\int\:_{1}^{e}\ln(12x)dx
area y=x^2,y=x^3	area\:y=x^{2},y=x^{3}
xy^'+y=-8xy^2	xy^{\prime\:}+y=-8xy^{2}
derivative of f(x)=x^2sin(sqrt(x))	derivative\:f(x)=x^{2}\sin(\sqrt{x})
integral of x+8	\int\:x+8dx
derivative of x^2-27	\frac{d}{dx}(x^{2}-27)
integral of ((4x+3)(2x^2+3x)^3)	\int\:((4x+3)(2x^{2}+3x)^{3})dx
(d^2)/(dx^2)((9x^2+6)^7)	\frac{d^{2}}{dx^{2}}((9x^{2}+6)^{7})
slope of (-2.5)(-4.1)	slope\:(-2.5)(-4.1)
derivative of 400x	\frac{d}{dx}(400x)
integral of csc^2(x)sqrt(3+cot(x))	\int\:\csc^{2}(x)\sqrt{3+\cot(x)}dx
(e^{-2x})^'	(e^{-2x})^{\prime\:}
derivative of 4x^2ln(x)	\frac{d}{dx}(4x^{2}\ln(x))
f(x)=sqrt(x+9)	f(x)=\sqrt{x+9}
derivative of x/(1+sqrt(x))	\frac{d}{dx}(\frac{x}{1+\sqrt{x}})
sum from n=4 to infinity of 1/(n^4)	\sum\:_{n=4}^{\infty\:}\frac{1}{n^{4}}
tangent of y=2xe^x,(0,0)	tangent\:y=2xe^{x},(0,0)
(dy)/(dx)=7y	\frac{dy}{dx}=7y
integral of sin(ln(x^2))	\int\:\sin(\ln(x^{2}))dx
(5x^2+3y+3y^2)dx+(x+2xy)dy=0	(5x^{2}+3y+3y^{2})dx+(x+2xy)dy=0
integral of (1+x)/(1+sqrt(x))	\int\:\frac{1+x}{1+\sqrt{x}}dx
(dy)/(dx)-y=xy^5	\frac{dy}{dx}-y=xy^{5}
integral of 14cos^3(x)	\int\:14\cos^{3}(x)dx
integral of (2x+1)	\int\:(2x+1)dx
limit as x approaches 3+of (3+x)/(3-x)	\lim\:_{x\to\:3+}(\frac{3+x}{3-x})
y^{'''}+18y^{''}+81y^'=0	y^{\prime\:\prime\:\prime\:}+18y^{\prime\:\prime\:}+81y^{\prime\:}=0
slope of (5,-1),(-5,5)	slope\:(5,-1),(-5,5)
derivative of \sqrt[3]{x^3-3x+c}	\frac{d}{dx}(\sqrt[3]{x^{3}-3x+c})
(dy)/(dx)-7=\sqrt[3]{y-7x+9}	\frac{dy}{dx}-7=\sqrt[3]{y-7x+9}
derivative of 3sqrt(x-1)	derivative\:3\sqrt{x-1}
integral of+5arctan(1/x)	\int\:+5\arctan(\frac{1}{x})dx
integral of (sec^2(x))/(tan^6(x))	\int\:\frac{\sec^{2}(x)}{\tan^{6}(x)}dx
sum from n=1 to infinity of 1/(n^{1.01)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{1.01}}
integral of 4piy(6+y^{3/2})	\int\:4πy(6+y^{\frac{3}{2}})dy
derivative of y=7x^2+3	derivative\:y=7x^{2}+3
derivative of e^xsin(2x+cos(2x)*2e^x)	\frac{d}{dx}(e^{x}\sin(2x)+\cos(2x)\cdot\:2e^{x})
limit as x approaches 3 of sqrt(25)	\lim\:_{x\to\:3}(\sqrt{25})
derivative of (x^2-2x+1(x^3-1))	\frac{d}{dx}((x^{2}-2x+1)(x^{3}-1))
integral from 0 to 2 of (-x^2+2x)	\int\:_{0}^{2}(-x^{2}+2x)dx
derivative of f(x)=2x^{-2}	derivative\:f(x)=2x^{-2}
sum from k=0 to infinity of 1/(2^k)	\sum\:_{k=0}^{\infty\:}\frac{1}{2^{k}}
limit as x approaches pi/3 of 2sin(x)	\lim\:_{x\to\:\frac{π}{3}}(2\sin(x))
derivative of x^2sin(x^2+3)	\frac{d}{dx}(x^{2}\sin(x^{2}+3))
integral of 1/(sqrt(5x+8))	\int\:\frac{1}{\sqrt{5x+8}}dx
inverse oflaplace 2/((s)(s+2))	inverselaplace\:\frac{2}{(s)(s+2)}
integral of x^2-25	\int\:x^{2}-25dx
derivative of sin^2(2x+1)	\frac{d}{dx}(\sin^{2}(2x+1))
derivative of (2x-1^2)	\frac{d}{dx}((2x-1)^{2})
xy^'-y= 4/3 xln(x)	xy^{\prime\:}-y=\frac{4}{3}x\ln(x)
integral of (x^2-x+36)/(x^3+6x)	\int\:\frac{x^{2}-x+36}{x^{3}+6x}dx
(\partial)/(\partial x)(10x(x^2+y^2)^{1/2})	\frac{\partial\:}{\partial\:x}(10x(x^{2}+y^{2})^{\frac{1}{2}})
(\partial)/(\partial x)((xy)/(1+x))	\frac{\partial\:}{\partial\:x}(\frac{xy}{1+x})
integral of-cos(x	\int\:-\cos(d)xdx
sum from n=0 to infinity of 1/(2n+4)	\sum\:_{n=0}^{\infty\:}\frac{1}{2n+4}
integral of 28x^3-15x^2+10x	\int\:28x^{3}-15x^{2}+10xdx
inverse oflaplace 5/(2(s-e)^2+50)	inverselaplace\:\frac{5}{2(s-e)^{2}+50}
inverse oflaplace (25)/(s^3(s^2+4s+5))	inverselaplace\:\frac{25}{s^{3}(s^{2}+4s+5)}
integral of (3x^2)/(5x^3-1)	\int\:\frac{3x^{2}}{5x^{3}-1}dx
integral of \sqrt[3]{x^2}-sqrt(x^3)	\int\:\sqrt[3]{x^{2}}-\sqrt{x^{3}}dx
y^'=(4x+y)^2	y^{\prime\:}=(4x+y)^{2}
(\partial)/(\partial x)(e^{xy}x)	\frac{\partial\:}{\partial\:x}(e^{xy}x)
derivative of sin(x+pi/2)	\frac{d}{dx}(\sin(x+\frac{π}{2}))
integral of (x^6-3x^2)^4(x^5-x)	\int\:(x^{6}-3x^{2})^{4}(x^{5}-x)dx
d/(dt)(3-3t)	\frac{d}{dt}(3-3t)
(\partial)/(\partial x)(cos(x)y)	\frac{\partial\:}{\partial\:x}(\cos(x)y)
area 5x,x^2-6	area\:5x,x^{2}-6
integral from 0 to 2pi of cos(2x)	\int\:_{0}^{2π}\cos(2x)dx
tangent of f(x)=sqrt(32-x)	tangent\:f(x)=\sqrt{32-x}
y^'-2y=e^{(2t)}	y^{\prime\:}-2\cdot\:y=e^{(2\cdot\:t)}
derivative of (3x+2/(4x))	\frac{d}{dx}(\frac{3x+2}{4x})
derivative of-sin(7x^2*14x)	\frac{d}{dx}(-\sin(7x^{2})\cdot\:14x)
(dx)/(dt)+2tx=t,x(0)= 3/2	\frac{dx}{dt}+2tx=t,x(0)=\frac{3}{2}
tangent of f(x)=5x^3+4x,\at x=-3	tangent\:f(x)=5x^{3}+4x,\at\:x=-3
f(x)=x*cos(x)	f(x)=x\cdot\:\cos(x)
derivative of ((x^2+3^5+x)^2)	\frac{d}{dx}(((x^{2}+3)^{5}+x)^{2})
derivative of (e^x)/(8+e^x)	derivative\:\frac{e^{x}}{8+e^{x}}
derivative of x+9/x	\frac{d}{dx}(x+\frac{9}{x})
tangent of y=9+3x+6xe^x	tangent\:y=9+3x+6xe^{x}
derivative of 6\sqrt[3]{x^2}	\frac{d}{dx}(6\sqrt[3]{x^{2}})
limit as x approaches 1/8 of 1/x-x^{-1}	\lim\:_{x\to\:\frac{1}{8}}(\frac{1}{x}-x^{-1})
integral of x^2(x+2)	\int\:x^{2}(x+2)dx
integral from 0 to 1 of xe^{8x}	\int\:_{0}^{1}xe^{8x}dx
integral of 7cos(x)+8sin(x)	\int\:7\cos(x)+8\sin(x)dx
integral of 1/(xsqrt(4-9ln^2(x)))	\int\:\frac{1}{x\sqrt{4-9\ln^{2}(x)}}dx
tangent of f(x)=sin(2x),\at x=-pi/3	tangent\:f(x)=\sin(2x),\at\:x=-\frac{π}{3}

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