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Popular Calculus Problems

area y= 4/(1+x^2),y=1	area\:y=\frac{4}{1+x^{2}},y=1
d/(dt)(t^2-2t)	\frac{d}{dt}(t^{2}-2t)
x^'=0.1078(1-x/(105900))x-0.1x	x^{\prime\:}=0.1078\cdot\:(1-\frac{x}{105900})x-0.1\cdot\:x
slope of (2.6)(5.15)	slope\:(2.6)(5.15)
limit as x approaches 1 of 2x^3-4x^2+x+9	\lim\:_{x\to\:1}(2x^{3}-4x^{2}+x+9)
tangent of 5x^2+x-5,\at x=8	tangent\:5x^{2}+x-5,\at\:x=8
sum from n=1 to infinity}(\frac{ln(n+4))/(n^{5/2)}}{1/(n^{5/2) of}	\sum\:_{n=1}^{\infty\:}\frac{\frac{\ln(n+4)}{n^{\frac{5}{2}}}}{\frac{1}{n^{\frac{5}{2}}}}
(\partial}{\partial x}(ln(\frac{xy)/z))	\frac{\partial\:}{\partial\:x}(\ln(\frac{xy}{z}))
integral of (e^{2x}+e^{-2x})^2	\int\:(e^{2x}+e^{-2x})^{2}dx
limit as x approaches 0 of arccos(x^2)	\lim\:_{x\to\:0}(\arccos(x^{2}))
integral of (1-3/x+y)	\int\:(1-\frac{3}{x}+y)dx
(dy)/(dt)=0.07y+200	\frac{dy}{dt}=0.07y+200
limit as x approaches infinity of-8x^6	\lim\:_{x\to\:\infty\:}(-8x^{6})
derivative of e^{x^2-2}	\frac{d}{dx}(e^{x^{2}-2})
integral of-8x+10y-3	\int\:-8x+10y-3dy
derivative of y=log_{3}(x)	derivative\:y=\log_{3}(x)
integral from 15 to 30 of 6	\int\:_{15}^{30}6dx
integral from 4 to 6 of 1	\int\:_{4}^{6}1
derivative of 3/(sqrt(2x+1))	\frac{d}{dx}(\frac{3}{\sqrt{2x+1}})
derivative of (x^2+2x+1/(x^2-2x+1))	\frac{d}{dx}(\frac{x^{2}+2x+1}{x^{2}-2x+1})
derivative of (3sqrt(x)+5x^2)	\frac{d}{dx}((3\sqrt{x}+5)x^{2})
y^{''}-6y^'+8y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+8y=0
integral of sin^7(x)cos^2(x)	\int\:\sin^{7}(x)\cos^{2}(x)dx
derivative of y=log_{5}(x)	derivative\:y=\log_{5}(x)
derivative of log_{10}(2x^2+5x+2)	\frac{d}{dx}(\log_{10}(2x^{2}+5x+2))
derivative of (3x-y)/x	derivative\:\frac{3x-y}{x}
(\partial)/(\partial x)(x^{0.2}y^{0.4})	\frac{\partial\:}{\partial\:x}(x^{0.2}y^{0.4})
limit as x approaches 3 of (3-x)/(x^2-9)	\lim\:_{x\to\:3}(\frac{3-x}{x^{2}-9})
integral of 1/(sqrt(x^2+4x+20))	\int\:\frac{1}{\sqrt{x^{2}+4x+20}}dx
derivative of f(t)=tsin(pit)	derivative\:f(t)=t\sin(πt)
integral of x^2tan(x^3)	\int\:x^{2}\tan(x^{3})dx
1/(x^6)(dy)/(dx)=25+20y	\frac{1}{x^{6}}\frac{dy}{dx}=25+20y
inverse oflaplace ((1-s^{-6})^2)/((1-s^{-1))^2}	inverselaplace\:\frac{(1-s^{-6})^{2}}{(1-s^{-1})^{2}}
(\partial)/(\partial y)(xzln(x+y+z))	\frac{\partial\:}{\partial\:y}(xz\ln(x+y+z))
(d^2)/(dx^2)(5cos(2x+10))	\frac{d^{2}}{dx^{2}}(5\cos(2x+10))
limit as q approaches 18 of 0.9q^2-6q+80	\lim\:_{q\to\:18}(0.9q^{2}-6q+80)
derivative of sec(θ)(θ-tan(θ))	derivative\:\sec(θ)(θ-\tan(θ))
derivative of sqrt(x^2+8)	derivative\:\sqrt{x^{2}+8}
f(x)=sqrt(x^2-10x+34)+sqrt(x^2+16)	f(x)=\sqrt{x^{2}-10x+34}+\sqrt{x^{2}+16}
integral of (sqrt(x)-3/x)^2x	\int\:(\sqrt{x}-\frac{3}{x})^{2}xdx
(\partial)/(\partial x)(xln(y)+y^2ln(x))	\frac{\partial\:}{\partial\:x}(x\ln(y)+y^{2}\ln(x))
d/(dy)(3x^2y^2+x/y)	\frac{d}{dy}(3x^{2}y^{2}+\frac{x}{y})
derivative of (3x^4-2(1+4x^3))	\frac{d}{dx}((3x^{4}-2)(1+4x^{3}))
derivative of-(14)/(x^3)	derivative\:-\frac{14}{x^{3}}
derivative of sqrt(4x^5+11)	derivative\:\sqrt{4x^{5}+11}
(\partial)/(\partial x)(-8d(J+1/2)^2)	\frac{\partial\:}{\partial\:x}(-8d(J+\frac{1}{2})^{2})
y^'-5y=e^{-2x}y^{-2}	y^{\prime\:}-5y=e^{-2x}y^{-2}
derivative of e^x+ln(x-1/x)	\frac{d}{dx}(e^{x}+\ln(x)-\frac{1}{x})
sum from n=1 to infinity of 1/((2n+3)^3)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n+3)^{3}}
tangent of f(x)=8(x-1/x),\at x=2	tangent\:f(x)=8(x-\frac{1}{x}),\at\:x=2
derivative of f(x^2(x))	\frac{d}{dx}(f(x)^{2}(x))
d/(dt)(t^3e^t)	\frac{d}{dt}(t^{3}e^{t})
derivative of (ln(x-1)^2)	\frac{d}{dx}((\ln(x)-1)^{2})
derivative of e^{3-5x}	\frac{d}{dx}(e^{3-5x})
derivative of 1/(x^{15})	\frac{d}{dx}(\frac{1}{x^{15}})
integral of (4x)/(sqrt(4x^2+3y^2))	\int\:\frac{4x}{\sqrt{4x^{2}+3y^{2}}}dx
derivative of arccos(7x)	\frac{d}{dx}(\arccos(7x))
tangent of y=1.8e^{2x}-41	tangent\:y=1.8e^{2x}-41
(\partial)/(\partial x)(xe^y-x^5+y-3)	\frac{\partial\:}{\partial\:x}(xe^{y}-x^{5}+y-3)
derivative of sinh(3x^2+1)	\frac{d}{dx}(\sinh(3x^{2}+1))
(dy)/(dx)=5y	\frac{dy}{dx}=5y
derivative of 2/((x-1)^3)	derivative\:\frac{2}{(x-1)^{3}}
area x^4,8x	area\:x^{4},8x
(cos(pi/x))^'	(\cos(\frac{π}{x}))^{\prime\:}
y^{''}+5y^'+4y=-8te^{2t}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=-8te^{2t}
integral from 0 to 2 of x/(x^2+4x+8)	\int\:_{0}^{2}\frac{x}{x^{2}+4x+8}dx
integral of 4e^{-t}	\int\:4e^{-t}dt
derivative of y=e^{6e^x}	derivative\:y=e^{6e^{x}}
derivative of-5x^{-2}	\frac{d}{dx}(-5x^{-2})
area x=y^2,x=4y-y^2	area\:x=y^{2},x=4y-y^{2}
integral of 2cos(x)	\int\:2\cos(x)dx
derivative of f(x)=(e^x)/(x^n)	derivative\:f(x)=\frac{e^{x}}{x^{n}}
integral from-1 to 1 of x/(sqrt(1-x^2))	\int\:_{-1}^{1}\frac{x}{\sqrt{1-x^{2}}}dx
derivative of xsqrt(x+5)	derivative\:x\sqrt{x+5}
derivative of f(x)=ln(sqrt((x+1)/(x-1)))	derivative\:f(x)=\ln(\sqrt{\frac{x+1}{x-1}})
integral of x^1(2+3x^2)^3	\int\:x^{1}(2+3x^{2})^{3}dx
slope of (5-1)(5-4)	slope\:(5-1)(5-4)
derivative of ((x^2+1)/x)	\frac{d}{dx}(\frac{(x^{2}+1)}{x})
integral of (x^2+3)cos(2x)	\int\:(x^{2}+3)\cos(2x)dx
derivative of (2cos(x)^2)	\frac{d}{dx}((2\cos(x))^{2})
integral from-1 to 1 of pi(e^x)^2	\int\:_{-1}^{1}π(e^{x})^{2}dx
derivative of 9x^{ln(9x)}	derivative\:9x^{\ln(9x)}
derivative of h(x)=e^x+x^5	derivative\:h(x)=e^{x}+x^{5}
limit as x approaches 5/2 of x^2+2x+4	\lim\:_{x\to\:\frac{5}{2}}(x^{2}+2x+4)
integral of cos((3x)/2)	\int\:\cos(\frac{3x}{2})dx
limit as x approaches-3 of 1/(x-3)	\lim\:_{x\to\:-3}(\frac{1}{x-3})
derivative of 2(x^'-ne^{-({p}(x,t)t)})	\frac{d}{dx}(2(x^{\prime\:}-n)e^{-({p}(x,t)t)})
derivative of x^{1/7}(x+8)	\frac{d}{dx}(x^{\frac{1}{7}}(x+8))
integral of 1/(x^2sqrt(x^2-14))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-14}}dx
integral from 2 to 3 of 1/(sqrt(3-x))	\int\:_{2}^{3}\frac{1}{\sqrt{3-x}}dx
(5y-2x)(dy)/(dx)-2y=0	(5y-2x)\frac{dy}{dx}-2y=0
slope of (3,-1/3),(8, 5/3)	slope\:(3,-\frac{1}{3}),(8,\frac{5}{3})
tangent of f(x)=e^x(-7-3x+5x^2),\at x=0	tangent\:f(x)=e^{x}(-7-3x+5x^{2}),\at\:x=0
derivative of 0.5(x+a)^p-x	derivative\:0.5(x+a)^{p}-x
integral of sin(3x-7)	\int\:\sin(3x-7)dx
d/(dt)(9cos(t))	\frac{d}{dt}(9\cos(t))
integral of 8sec^4(x)	\int\:8\sec^{4}(x)dx
integral of 1+sin(θ)	\int\:1+\sin(θ)dθ
f(x)=sin(x)-cos(x)	f(x)=\sin(x)-\cos(x)
derivative of y=sqrt(-2x^2+32x-7)	derivative\:y=\sqrt{-2x^{2}+32x-7}

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