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Popular Calculus Problems

integral of tanh(2x)ln(cosh(2x))	\int\:\tanh(2x)\ln(\cosh(2x))dx
area cos(x),x^2+2,[1,2]	area\:\cos(x),x^{2}+2,[1,2]
integral of 5/(x(x^2+2)^2)	\int\:\frac{5}{x(x^{2}+2)^{2}}dx
inverse oflaplace s/(s^2+s)	inverselaplace\:\frac{s}{s^{2}+s}
integral of (x^2)/2*1/x	\int\:\frac{x^{2}}{2}\cdot\:\frac{1}{x}dx
laplacetransform 2e^{-5t}sin(2t)	laplacetransform\:2e^{-5t}\sin(2t)
y^'=3\sqrt[3]{y^2}	y^{\prime\:}=3\sqrt[3]{y^{2}}
derivative of f(x)=xln(x^2)	derivative\:f(x)=x\ln(x^{2})
slope of (-2,-4),(-3,-3)	slope\:(-2,-4),(-3,-3)
(\partial)/(\partial x)(e^xx)	\frac{\partial\:}{\partial\:x}(e^{x}x)
(\partial)/(\partial y)(-1/y)	\frac{\partial\:}{\partial\:y}(-\frac{1}{y})
(dy)/(dt)=y(1-0.0002y)	\frac{dy}{dt}=y(1-0.0002y)
integral of 2^xx	\int\:2^{x}xdx
y^{''}-2y^'+5y=0,y(pi)=0,y^'(pi)=2	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=0,y(π)=0,y^{\prime\:}(π)=2
tangent of f(x)=3x^2,\at x=4	tangent\:f(x)=3x^{2},\at\:x=4
derivative of (x+5/(sqrt(x)))	\frac{d}{dx}(\frac{x+5}{\sqrt{x}})
x^2y^{''}+xy^'-y=x^{1/2}	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=x^{\frac{1}{2}}
limit as x approaches infinity of (4^x+3)/(4^{x+1)}	\lim\:_{x\to\:\infty\:}(\frac{4^{x}+3}{4^{x+1}})
derivative of f(x)=-2/x	derivative\:f(x)=-\frac{2}{x}
integral of (csc(x))	\int\:(\csc(x))dx
derivative of arctan(sqrt(-5x+1))	\frac{d}{dx}(\arctan(\sqrt{-5x+1}))
derivative of f(x)=3x^2+5x-6	derivative\:f(x)=3x^{2}+5x-6
derivative of (6x/(7-cot(x)))	\frac{d}{dx}(\frac{6x}{7-\cot(x)})
(\partial)/(\partial x)(x^{yz})	\frac{\partial\:}{\partial\:x}(x^{yz})
derivative of (-6/(x^4))	\frac{d}{dx}(\frac{-6}{x^{4}})
derivative of x^4tan(x-sqrt(x))	\frac{d}{dx}(x^{4}\tan(x)-\sqrt{x})
derivative of ((e^{2x})/2)	\frac{d}{dx}(\frac{(e^{2x})}{2})
integral of 12(e^{0.02x}-1)	\int\:12(e^{0.02x}-1)dx
derivative of 2x^{-5}	derivative\:2x^{-5}
integral of-2cos(x)	\int\:-2\cos(x)dx
integral from 1 to 6 of sqrt(x-1)	\int\:_{1}^{6}\sqrt{x-1}dx
derivative of y=(13x^2-26x+26)e^{-8x}	derivative\:y=(13x^{2}-26x+26)e^{-8x}
integral of 36-x^2	\int\:36-x^{2}dx
derivative of ((x+2)/(sqrt(2-x)))	\frac{d}{dx}(\frac{(x+2)}{\sqrt{2-x}})
y^{''}+4y=12sin(2t)	y^{\prime\:\prime\:}+4y=12\sin(2t)
integral of e^{3x}(3x+1)	\int\:e^{3x}(3x+1)dx
integral from 0 to t of cos^2(wt)	\int\:_{0}^{t}\cos^{2}(wt)dt
integral of 3ay^2	\int\:3ay^{2}dy
derivative of (x+5/(x-1))	\frac{d}{dx}(\frac{x+5}{x-1})
limit as x approaches 0 of sin((pix)/2)	\lim\:_{x\to\:0}(\sin(\frac{πx}{2}))
integral of (3x^2)/(sqrt(x^2-5))	\int\:\frac{3x^{2}}{\sqrt{x^{2}-5}}dx
derivative of f(3)= 1/x+(x^2-1)^3	derivative\:f(3)=\frac{1}{x}+(x^{2}-1)^{3}
limit as x approaches 9 of 4-sqrt(x)+7	\lim\:_{x\to\:9}(4-\sqrt{x}+7)
limit as x approaches 0+of (e^{ax}+x)^{1/x}	\lim\:_{x\to\:0+}((e^{ax}+x)^{\frac{1}{x}})
(\partial)/(\partial x)(y/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{y}{x-y})
integral from 1 to infinity of xe^{-7x}	\int\:_{1}^{\infty\:}xe^{-7x}dx
y^'+4y=6e^{-3t}	y^{\prime\:}+4y=6e^{-3t}
limit as y approaches-3 of sqrt((y^2-9)/(2y^2+7y+3))	\lim\:_{y\to\:-3}(\sqrt{\frac{y^{2}-9}{2y^{2}+7y+3}})
16y^{''}-y=0,y(-7)=1,y^'(-7)=-1	16y^{\prime\:\prime\:}-y=0,y(-7)=1,y^{\prime\:}(-7)=-1
derivative of x^{5/3}-5x^{2/3}	\frac{d}{dx}(x^{\frac{5}{3}}-5x^{\frac{2}{3}})
derivative of tan(x+1/x)	\frac{d}{dx}(\tan(x)+\frac{1}{x})
derivative of y=\sqrt[8]{x}	derivative\:y=\sqrt[8]{x}
limit as x approaches pi-of csc(x)	\lim\:_{x\to\:π-}(\csc(x))
integral from 0 to 1 of 1/(sqrt(4-t^2))	\int\:_{0}^{1}\frac{1}{\sqrt{4-t^{2}}}dt
tangent of y= 5/(x^3)	tangent\:y=\frac{5}{x^{3}}
derivative of (3x^{4x})	\frac{d}{dx}((3x)^{4x})
derivative of cx^{-7}	\frac{d}{dx}(cx^{-7})
(dy)/(dx)=(sec(y))/((x+2)^2)	\frac{dy}{dx}=\frac{\sec(y)}{(x+2)^{2}}
integral of k/(x^4)	\int\:\frac{k}{x^{4}}dx
(\partial)/(\partial y)(2x-4y)	\frac{\partial\:}{\partial\:y}(2x-4y)
integral of (4x^2+3)/(0.4x^3+0.9x)	\int\:\frac{4x^{2}+3}{0.4x^{3}+0.9x}dx
d/(dt)((t^3-2t^2+2t-4)/(t^2+2))	\frac{d}{dt}(\frac{t^{3}-2t^{2}+2t-4}{t^{2}+2})
derivative of sin(θ)	derivative\:\sin(θ)
y^'=y^2+3	y^{\prime\:}=y^{2}+3
derivative of-xe^{-2xy}	\frac{d}{dx}(-xe^{-2xy})
limit as x approaches 2 of 3x+1	\lim\:_{x\to\:2}(3x+1)
integral of (x-1)/(sqrt(2x)-\sqrt{x+1)}	\int\:\frac{x-1}{\sqrt{2x}-\sqrt{x+1}}dx
derivative of 2xe^{-2x}	\frac{d}{dx}(2xe^{-2x})
sum from n=5 to infinity of (5^n)/(6^n)	\sum\:_{n=5}^{\infty\:}\frac{5^{n}}{6^{n}}
integral of 28(7x-2)^{-5}	\int\:28(7x-2)^{-5}dx
(\partial)/(\partial x)(((2x-2y))/(4x+2y))	\frac{\partial\:}{\partial\:x}(\frac{(2x-2y)}{4x+2y})
(\partial)/(\partial x)(t^2e^{(x^2)/(2t)})	\frac{\partial\:}{\partial\:x}(t^{2}e^{\frac{x^{2}}{2t}})
area-x,-10x+14,x=0	area\:-x,-10x+14,x=0
maclaurin x^3e^{2x}	maclaurin\:x^{3}e^{2x}
sum from n=0 to infinity of (x^n)/(3*n)	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{3\cdot\:n}
derivative of y= 3/(sqrt(x))	derivative\:y=\frac{3}{\sqrt{x}}
y^'=3x^2e^{-y}	y^{\prime\:}=3x^{2}e^{-y}
integral of 1/(xln(x^6))	\int\:\frac{1}{x\ln(x^{6})}dx
integral of x/((x+5)^2)	\int\:\frac{x}{(x+5)^{2}}dx
derivative of (12x^2-24x+24e^x)	\frac{d}{dx}((12x^{2}-24x+24)e^{x})
derivative of (2/3 ^x)	\frac{d}{dx}((\frac{2}{3})^{x})
derivative of f(x)=(4x-3)(sqrt(x)+2)	derivative\:f(x)=(4x-3)(\sqrt{x}+2)
derivative of f(x)=x^2+10	derivative\:f(x)=x^{2}+10
integral of sec^2(x)tan^{10}(x)	\int\:\sec^{2}(x)\tan^{10}(x)dx
taylor e^{(x+1)}	taylor\:e^{(x+1)}
limit as x approaches 5 of 6	\lim\:_{x\to\:5}(6)
x^{''}+2x^'+4x=0	x^{\prime\:\prime\:}+2x^{\prime\:}+4x=0
d/(dz)((z+i)/(z-i))	\frac{d}{dz}(\frac{z+i}{z-i})
limit as x approaches-1 of 3x^2-2x^2+4	\lim\:_{x\to\:-1}(3x^{2}-2x^{2}+4)
laplacetransform e^3e^t(-sin(pit))	laplacetransform\:e^{3}e^{t}(-\sin(πt))
y^'=y^2-4	y^{\prime\:}=y^{2}-4
integral from 1 to R of x^{-8/5}	\int\:_{1}^{R}x^{-\frac{8}{5}}dx
integral of x^0	\int\:x^{0}dx
derivative of cos(arctan(6x))	\frac{d}{dx}(\cos(\arctan(6x)))
derivative of x^4(7-x^2^3)	\frac{d}{dx}(x^{4}(7-x^{2})^{3})
integral of arctan(tan(x))	\int\:\arctan(\tan(x))dx
integral of (45)/(1-cos(5x))	\int\:\frac{45}{1-\cos(5x)}dx
simplify-4	simplify\:-4
derivative of f(-1)=-x^3	derivative\:f(-1)=-x^{3}
tangent of f(x)=x^3-3x+1,(4,53)	tangent\:f(x)=x^{3}-3x+1,(4,53)

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