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Popular Calculus Problems

f(x)=sin(xcos(x))	f(x)=\sin(x\cos(x))
t(dy)/(dt)+2y=sin(t)	t\frac{dy}{dt}+2y=\sin(t)
integral from 0 to 3 of (e^x)	\int\:_{0}^{3}(e^{x})dx
integral of (4x^3+5x)e^{x^2}	\int\:(4x^{3}+5x)e^{x^{2}}dx
integral of (x^2)/(x^{3+1)}	\int\:\frac{x^{2}}{x^{3+1}}dx
integral of 1/3 e^t	\int\:\frac{1}{3}e^{t}dt
x^2+x(dy)/(dx)=y	x^{2}+x\frac{dy}{dx}=y
(\partial)/(\partial y)(-3y)	\frac{\partial\:}{\partial\:y}(-3y)
y^'+t/(t^2-16)y=(e^t)/(t-9)	y^{\prime\:}+\frac{t}{t^{2}-16}y=\frac{e^{t}}{t-9}
sum from n=0 to infinity of cos(npi)	\sum\:_{n=0}^{\infty\:}\cos(nπ)
integral from 0 to infinity of 8/(x^2+4)	\int\:_{0}^{\infty\:}\frac{8}{x^{2}+4}dx
derivative of x*sqrt(x^2+1)	\frac{d}{dx}(x\cdot\:\sqrt{x^{2}+1})
tangent of y=xsqrt(x),(1,1)	tangent\:y=x\sqrt{x},(1,1)
derivative of x/(sin(x))	\frac{d}{dx}(\frac{x}{\sin(x)})
(\partial)/(\partial x)(x^{1/4})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{4}})
limit as x approaches 1 of 2x+3	\lim\:_{x\to\:1}(2x+3)
derivative of (5x^3/4-2/(5x^3))	\frac{d}{dx}(\frac{5x^{3}}{4}-\frac{2}{5x^{3}})
integral of (ln(x^2))	\int\:(\ln(x^{2}))dx
integral of (((x^m-x^n)^2)/(sqrt(x)))	\int\:(\frac{(x^{m}-x^{n})^{2}}{\sqrt{x}})dx
(\partial)/(\partial y)(4x^2+2xy+y^2-8)	\frac{\partial\:}{\partial\:y}(4x^{2}+2xy+y^{2}-8)
derivative of x^5e^{xy}+3x	\frac{d}{dx}(x^{5}e^{xy}+3x)
f(x)=tan(5x)	f(x)=\tan(5x)
derivative of ln(sqrt(((x-3))/(x-1)))	derivative\:\ln(\sqrt{\frac{(x-3)}{x-1}})
integral of t^3cos(t^2)	\int\:t^{3}\cos(t^{2})dt
limit as x approaches 5+of (5-x)/(\|5-x\|)	\lim\:_{x\to\:5+}(\frac{5-x}{\left\|5-x\right\|})
derivative of ln(4x+7)	derivative\:\ln(4x+7)
integral of ((3+e^x)^2)/(e^x)	\int\:\frac{(3+e^{x})^{2}}{e^{x}}dx
(\partial)/(\partial x)(-ysin(x))	\frac{\partial\:}{\partial\:x}(-y\sin(x))
derivative of (sin(2x)/(tan(x)))	\frac{d}{dx}(\frac{\sin(2x)}{\tan(x)})
taylor 1/((x+2))	taylor\:\frac{1}{(x+2)}
integral of 1/(\sqrt[4]{x+2)}	\int\:\frac{1}{\sqrt[4]{x+2}}dx
integral of 3/(x^2(x^2+25))	\int\:\frac{3}{x^{2}(x^{2}+25)}dx
integral of 1/(36+x^2)	\int\:\frac{1}{36+x^{2}}dx
(\partial)/(\partial x)(-2e^{4y-x^2-y^2}x)	\frac{\partial\:}{\partial\:x}(-2e^{4y-x^{2}-y^{2}}x)
limit as x approaches infinity of x-6	\lim\:_{x\to\:\infty\:}(x-6)
area (8cos(pix)),(8x^2-2),[-0.5,0.5]	area\:(8\cos(πx)),(8x^{2}-2),[-0.5,0.5]
(\partial)/(\partial y)((x-4)ln(xy))	\frac{\partial\:}{\partial\:y}((x-4)\ln(xy))
integral from 0 to ln(4) of (e^x)/(sqrt(e^{2x)+25)}	\int\:_{0}^{\ln(4)}\frac{e^{x}}{\sqrt{e^{2x}+25}}dx
limit as x approaches-infinity of 1/x+3	\lim\:_{x\to\:-\infty\:}(\frac{1}{x}+3)
derivative of 4xe^{3x}	\frac{d}{dx}(4xe^{3x})
derivative of x/(sin(x+cos(x)))	\frac{d}{dx}(\frac{x}{\sin(x)+\cos(x)})
derivative of e^{5x}cos(3x)	\frac{d}{dx}(e^{5x}\cos(3x))
derivative of (x^4/(3-x^3))	\frac{d}{dx}(\frac{x^{4}}{3-x^{3}})
derivative of-4e^{-4x}	\frac{d}{dx}(-4e^{-4x})
derivative of sqrt(7x-8)	\frac{d}{dx}(\sqrt{7x-8})
sum from n=0 to infinity of (400)(0.1)^n	\sum\:_{n=0}^{\infty\:}(400)(0.1)^{n}
(dy)/(dx)=(x^2+2)/(3y^2)	\frac{dy}{dx}=\frac{x^{2}+2}{3y^{2}}
(x^2+x)^'	(x^{2}+x)^{\prime\:}
derivative of ((x^2)/(sin(x)))	\frac{d}{dx}(\frac{(x^{2})}{\sin(x)})
y^'-e^{6x+y}=0	y^{\prime\:}-e^{6x+y}=0
integral of x(x+1)^4	\int\:x(x+1)^{4}dx
(arcsin(2x))^'	(\arcsin(2x))^{\prime\:}
y^{''}-9y=e^{3x}	y^{\prime\:\prime\:}-9y=e^{3x}
derivative of {y}(θ,xtan(θ))	\frac{d}{dx}({y}(θ,x)\tan(θ))
y(dy)/(dx)-y^3=y^2ln(x)	y\frac{dy}{dx}-y^{3}=y^{2}\ln(x)
derivative of (x-2^2+2)	\frac{d}{dx}((x-2)^{2}+2)
y^'+5y=e^{-3t}	y^{\prime\:}+5y=e^{-3t}
inverse oflaplace (s+2)/((s-1)(s+3)^2)	inverselaplace\:\frac{s+2}{(s-1)(s+3)^{2}}
integral of (sqrt(x+1))/(x+10)	\int\:\frac{\sqrt{x+1}}{x+10}dx
area f(x)=x^2,(0,3)	area\:f(x)=x^{2},(0,3)
integral of 1/(e^xsqrt(e^{2x)-9)}	\int\:\frac{1}{e^{x}\sqrt{e^{2x}-9}}dx
integral of x^{15}	\int\:x^{15}dx
derivative of (7x^2-12xe^x)	\frac{d}{dx}((7x^{2}-12x)e^{x})
(\partial)/(\partial y)(4x^3-5x^2+8x)	\frac{\partial\:}{\partial\:y}(4x^{3}-5x^{2}+8x)
(e^{-x}sin(x))^'	(e^{-x}\sin(x))^{\prime\:}
integral of 4xcos(x)	\int\:4x\cos(x)dx
integral from-2 to 3 of 3/(x^4)	\int\:_{-2}^{3}\frac{3}{x^{4}}dx
(\partial)/(\partial x)(v)	\frac{\partial\:}{\partial\:x}(v)
sum from n=0 to infinity of (-1)^nx^{3n}	\sum\:_{n=0}^{\infty\:}(-1)^{n}x^{3n}
limit as (x,y) approaches (1,1) of x+y	\lim\:_{(x,y)\to\:(1,1)}(x+y)
derivative of (x^2^{2x})	\frac{d}{dx}((x^{2})^{2x})
inverse oflaplace (8s^2-4s+12)/(s(s^2+4))	inverselaplace\:\frac{8s^{2}-4s+12}{s(s^{2}+4)}
tangent of f(x)=sqrt(x),\at x= 49/121	tangent\:f(x)=\sqrt{x},\at\:x=\frac{49}{121}
(d^4)/(dx^4)(2e^{x^2})	\frac{d^{4}}{dx^{4}}(2e^{x^{2}})
(\partial)/(\partial y)(y+xy)	\frac{\partial\:}{\partial\:y}(y+xy)
limit as x approaches-4 of (x^2+3x-4)/(x+4)	\lim\:_{x\to\:-4}(\frac{x^{2}+3x-4}{x+4})
tangent of-x^2+1	tangent\:-x^{2}+1
derivative of e^{x^4+7x}	\frac{d}{dx}(e^{x^{4}+7x})
(\partial)/(\partial x)(7+xln(xy-9))	\frac{\partial\:}{\partial\:x}(7+x\ln(xy-9))
derivative of (x^3+5x^2-x^{-2}+8^{-7/6})	\frac{d}{dx}((x^{3}+5x^{2}-x^{-2}+8)^{-\frac{7}{6}})
limit as q approaches 0+of sqrt(4q)	\lim\:_{q\to\:0+}(\sqrt{4q})
integral of 22x^{21}	\int\:22x^{21}dx
limit as x approaches 8 of x^{8/3}	\lim\:_{x\to\:8}(x^{\frac{8}{3}})
(2x-x^{-2}y)dx+x^{-1}dy=0	(2x-x^{-2}y)dx+x^{-1}dy=0
integral of (2x^3+x^2+4)/((x^2+4)^2)	\int\:\frac{2x^{3}+x^{2}+4}{(x^{2}+4)^{2}}dx
(\partial)/(\partial x)(xe^y-ln(x))	\frac{\partial\:}{\partial\:x}(xe^{y}-\ln(x))
derivative of (4x^2-3/(x-1))	\frac{d}{dx}(\frac{4x^{2}-3}{x-1})
d/(dt)((sin(t)+cos(t))^2)	\frac{d}{dt}((\sin(t)+\cos(t))^{2})
slope of y=5x^2+6/x	slope\:y=5x^{2}+\frac{6}{x}
derivative of y=(8t)/(8+sqrt(t))	derivative\:y=\frac{8t}{8+\sqrt{t}}
limit as x approaches 2 of 2xe^{x^2}	\lim\:_{x\to\:2}(2xe^{x^{2}})
integral of 2x^3(1-x^4)^{-1/4}	\int\:2x^{3}(1-x^{4})^{-\frac{1}{4}}dx
integral of x/(sqrt(9-4x^2))	\int\:\frac{x}{\sqrt{9-4x^{2}}}dx
integral of ((1+6ln(x))^2)/x	\int\:\frac{(1+6\ln(x))^{2}}{x}dx
(dy)/(dx)=(x^2y^2)/(1+x)	\frac{dy}{dx}=\frac{x^{2}y^{2}}{1+x}
integral from 0 to 5 of 2x^2e^{-x}	\int\:_{0}^{5}2x^{2}e^{-x}dx
derivative of 3t(2t^2-5)^4	derivative\:3t(2t^{2}-5)^{4}
inverse oflaplace ((s-2))/((s-2)^2+1)	inverselaplace\:\frac{(s-2)}{(s-2)^{2}+1}
(\partial)/(\partial x)(e^{2x+y})	\frac{\partial\:}{\partial\:x}(e^{2x+y})
tangent of f(x)=7x-6sqrt(x),\at x=1	tangent\:f(x)=7x-6\sqrt{x},\at\:x=1

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