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Popular Calculus Problems

integral from 1 to 2 of 2/(x^3+4x)	\int\:_{1}^{2}\frac{2}{x^{3}+4x}dx
(\partial)/(\partial y)(x^2*y^2)	\frac{\partial\:}{\partial\:y}(x^{2}\cdot\:y^{2})
y^{''}-7y^'-18y=0	y^{\prime\:\prime\:}-7y^{\prime\:}-18y=0
limit as x approaches 2 of ((x+2))/(3x)	\lim\:_{x\to\:2}(\frac{(x+2)}{3x})
(\partial)/(\partial y)(y^2cos(x))	\frac{\partial\:}{\partial\:y}(y^{2}\cos(x))
(\partial)/(\partial x)(6tan(xy))	\frac{\partial\:}{\partial\:x}(6\tan(xy))
sum from n=1 to infinity of sin(1/(2^n))	\sum\:_{n=1}^{\infty\:}\sin(\frac{1}{2^{n}})
laplacetransform 2*cos(5t)	laplacetransform\:2\cdot\:\cos(5t)
(\partial)/(\partial y)(e^{5x}sin(5y))	\frac{\partial\:}{\partial\:y}(e^{5x}\sin(5y))
integral of-4tan(x)	\int\:-4\tan(x)dx
integral of 35sec^{-2}(xta)n^3x	\int\:35\sec^{-2}(xta)n^{3}xdx
limit as x approaches 1 of (1-x)/(x^2-1)	\lim\:_{x\to\:1}(\frac{1-x}{x^{2}-1})
(-1/x)^'	(-\frac{1}{x})^{\prime\:}
y^{''}+2y^'=2x+9-e^{-2x}	y^{\prime\:\prime\:}+2y^{\prime\:}=2x+9-e^{-2x}
inverse oflaplace (6s+4)/(s^2+4s+20)	inverselaplace\:\frac{6s+4}{s^{2}+4s+20}
y^'+5y=e^{-3x}	y^{\prime\:}+5y=e^{-3x}
integral of sin^6(x)cos^5(x)	\int\:\sin^{6}(x)\cos^{5}(x)dx
integral of e^x+x^e+e+x	\int\:e^{x}+x^{e}+e+xdx
derivative of f(x)=sin(4x)-cos(3x)	derivative\:f(x)=\sin(4x)-\cos(3x)
(dy)/(dx)=x^3+x^2-5x+11	\frac{dy}{dx}=x^{3}+x^{2}-5x+11
integral from 1 to 1000 of (21)/(x^3)	\int\:_{1}^{1000}\frac{21}{x^{3}}dx
y^{''}-2y^'+5y=e^tcos(2t)	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=e^{t}\cos(2t)
laplacetransform (sin(6t)-7)^2	laplacetransform\:(\sin(6t)-7)^{2}
integral of (cos^2(θ))/(sin(θ))	\int\:\frac{\cos^{2}(θ)}{\sin(θ)}dθ
derivative of f(x)=2^{90}	derivative\:f(x)=2^{90}
limit as x approaches 5+of x^3-cx	\lim\:_{x\to\:5+}(x^{3}-cx)
derivative of f(x)=x+4/x	derivative\:f(x)=x+\frac{4}{x}
2y^{''}-4y^'+3y=9t^2+10	2y^{\prime\:\prime\:}-4y^{\prime\:}+3y=9t^{2}+10
derivative of 3^{3x+1}	\frac{d}{dx}(3^{3x+1})
integral of x^6y^2	\int\:x^{6}y^{2}
derivative of x^2+7x-4	derivative\:x^{2}+7x-4
limit as x approaches-infinity of 6x^4	\lim\:_{x\to\:-\infty\:}(6x^{4})
limit as x approaches infinity of-5/4	\lim\:_{x\to\:\infty\:}(-\frac{5}{4})
derivative of (\sqrt[3]{t})/(t-6)	derivative\:\frac{\sqrt[3]{t}}{t-6}
taylor (1-x)^{1/4}	taylor\:(1-x)^{\frac{1}{4}}
sum from n=1 to infinity of (1/8)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{8})^{n-1}
derivative of (ce^x/(1+ce^x))	\frac{d}{dx}(\frac{ce^{x}}{1+ce^{x}})
tangent of y=x^2+7,(3,16)	tangent\:y=x^{2}+7,(3,16)
derivative of x^3+2x+1	\frac{d}{dx}(x^{3}+2x+1)
integral of sin(3x+2)	\int\:\sin(3x+2)dx
tangent of y=4xcos(x),\at x=pi	tangent\:y=4x\cos(x),\at\:x=π
integral of 1/(csc^2(x))	\int\:\frac{1}{\csc^{2}(x)}dx
slope ofintercept (2.1)(8.7)	slopeintercept\:(2.1)(8.7)
(\partial)/(\partial x)(sin(3x-2y))	\frac{\partial\:}{\partial\:x}(\sin(3x-2y))
derivative of ln(x^2-x)	\frac{d}{dx}(\ln(x^{2}-x))
tangent of y=-3cos(x),\at x=(-pi)/3	tangent\:y=-3\cos(x),\at\:x=\frac{-π}{3}
(e^y+1)^2e^{-y}dx+(e^x+1)^3dy=0	(e^{y}+1)^{2}e^{-y}dx+(e^{x}+1)^{3}dy=0
integral of 4e^x+12x^3+4x	\int\:4e^{x}+12x^{3}+4xdx
tangent of f(x)=2sin(x),\at x= pi/4	tangent\:f(x)=2\sin(x),\at\:x=\frac{π}{4}
slope of (5.2)(-9.6)	slope\:(5.2)(-9.6)
derivative of e^{x^2-x}	derivative\:e^{x^{2}-x}
slope of y=3+4x^2-2x^3x=a	slope\:y=3+4x^{2}-2x^{3}x=a
limit as x approaches-infinity of-3x	\lim\:_{x\to\:-\infty\:}(-3x)
sum from n=1 to infinity of (10)/n	\sum\:_{n=1}^{\infty\:}\frac{10}{n}
limit as x approaches 0 of (tan(0))/0	\lim\:_{x\to\:0}(\frac{\tan(0)}{0})
derivative of 1/(sqrt(x+7))	derivative\:\frac{1}{\sqrt{x+7}}
derivative of x/(7x+9)	\frac{d}{dx}(\frac{x}{7x+9})
integral of 0.2t^2	\int\:0.2t^{2}dt
integral of (θ-csc(θ)cot(θ))	\int\:(θ-\csc(θ)\cot(θ))dθ
limit as x approaches infinity of (1)^x	\lim\:_{x\to\:\infty\:}((1)^{x})
integral of 4/(x^3-2x^2)	\int\:\frac{4}{x^{3}-2x^{2}}dx
xy^'-2y=6x^2	xy^{\prime\:}-2y=6x^{2}
integral of f(x,y,z)	\int\:f(x,y,z)dx
derivative of \sqrt[7]{x}+6sqrt(x^7)	\frac{d}{dx}(\sqrt[7]{x}+6\sqrt{x^{7}})
integral of 1/(sqrt(100-x^2))	\int\:\frac{1}{\sqrt{100-x^{2}}}dx
(\partial)/(\partial x)((-y^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{-y^{2}}{(x-y)^{2}})
integral of e^{i7x}cos(5x)	\int\:e^{i7x}\cos(5x)dx
(\partial)/(\partial x)(5e^{x-y})	\frac{\partial\:}{\partial\:x}(5e^{x-y})
integral of 3/((x^2+1)^{3/2)}	\int\:\frac{3}{(x^{2}+1)^{\frac{3}{2}}}dx
integral of (2u)/(1+u^2)	\int\:\frac{2u}{1+u^{2}}du
y^{''}+y^'-2y=2x	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2x
integral of 2e^u	\int\:2e^{u}du
((3y^2-x^2))/(y^5)y^'+x/(2y^4)=0	\frac{(3y^{2}-x^{2})}{y^{5}}y^{\prime\:}+\frac{x}{2y^{4}}=0
derivative of f(x)=-5.7+3.57ln(x)	derivative\:f(x)=-5.7+3.57\ln(x)
integral of sqrt(1+cos^2(x))	\int\:\sqrt{1+\cos^{2}(x)}dx
derivative of (3x-1/(x+1))	\frac{d}{dx}(\frac{3x-1}{x+1})
integral of x/((1+x^2)^{1/2)}	\int\:\frac{x}{(1+x^{2})^{\frac{1}{2}}}dx
derivative of 8(0.9^{x-2})	\frac{d}{dx}(8(0.9)^{x-2})
xy^'=y^2-y,y(2)=1	xy^{\prime\:}=y^{2}-y,y(2)=1
integral from 0 to 1 of 1/((x^2+1)^3)	\int\:_{0}^{1}\frac{1}{(x^{2}+1)^{3}}dx
tangent of f(x)=3x^2-5x+8,\at x=2	tangent\:f(x)=3x^{2}-5x+8,\at\:x=2
inverse oflaplace 2/((s^2-1)(s-1))	inverselaplace\:\frac{2}{(s^{2}-1)(s-1)}
(\partial)/(\partial y)(x^2+5y^2)	\frac{\partial\:}{\partial\:y}(x^{2}+5y^{2})
limit as x approaches 3-of-3/7 x+4/11	\lim\:_{x\to\:3-}(-\frac{3}{7}x+\frac{4}{11})
(\partial)/(\partial z)(x/(sqrt(y+z)))	\frac{\partial\:}{\partial\:z}(\frac{x}{\sqrt{y+z}})
limit as x approaches 0-of ((x+4))/((3))	\lim\:_{x\to\:0-}(\frac{(x+4)}{(3)})
9y^{''}-30y^'+25y=0	9y^{\prime\:\prime\:}-30y^{\prime\:}+25y=0
integral of 2/5 x^{5/2}-54/5	\int\:\frac{2}{5}x^{\frac{5}{2}}-\frac{54}{5}dx
(\partial)/(\partial x)(y+1/x)	\frac{\partial\:}{\partial\:x}(y+\frac{1}{x})
integral of e^{-yx}	\int\:e^{-yx}dx
derivative of (6x/(x-1))	\frac{d}{dx}(\frac{6x}{x-1})
integral of ye^x+sin(y)	\int\:ye^{x}+\sin(y)dx
integral from 0 to 2 of 2x^2sqrt(x^3+1)	\int\:_{0}^{2}2x^{2}\sqrt{x^{3}+1}dx
integral of 6/(5\sqrt[3]{x)}	\int\:\frac{6}{5\sqrt[3]{x}}dx
y^{''}+16y=24sec(4t)	y^{\prime\:\prime\:}+16y=24\sec(4t)
limit as x approaches-4+of f(x)	\lim\:_{x\to\:-4+}(f(x))
tangent of x^2+xy+2y^2=32,(5,1)	tangent\:x^{2}+xy+2y^{2}=32,(5,1)
derivative of sin^3(2x+1)	\frac{d}{dx}(\sin^{3}(2x+1))
integral from 1 to 3 of x^3	\int\:_{1}^{3}x^{3}dx
inverse oflaplace 5/((s+4)^2(s+1))	inverselaplace\:\frac{5}{(s+4)^{2}(s+1)}

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