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Popular Calculus Problems

integral of sqrt(4x-1)	\int\:\sqrt{4x-1}dx
derivative of (x^2+1^{sin(x)})	\frac{d}{dx}((x^{2}+1)^{\sin(x)})
integral from 0 to 1 of 2(1+sqrt(x))^5	\int\:_{0}^{1}2(1+\sqrt{x})^{5}dx
derivative of 0.8e^xarctan(x)	derivative\:0.8e^{x}\arctan(x)
integral of ((x+1))/(x-1)	\int\:\frac{(x+1)}{x-1}dx
(d^3)/(dx^3)(8/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{8}{x^{2}})
integral of 9xe^{7x}	\int\:9xe^{7x}dx
integral of 1/(y^2-y-2)	\int\:\frac{1}{y^{2}-y-2}dy
y^{'''}-3y^{''}+3y^'-y=x-7e^x	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=x-7e^{x}
derivative of 4+x^2	\frac{d}{dx}(4+x^{2})
(16xy-3x^2)dx+(8x^2+2y)dy=0	(16xy-3x^{2})dx+(8x^{2}+2y)dy=0
derivative of 6x^2cos(xcot(x))	\frac{d}{dx}(6x^{2}\cos(x)\cot(x))
sum from n=1 to infinity of 1/(n^3+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{3}+1}
integral of ((3x^4))/((x^2-2x))	\int\:\frac{(3x^{4})}{(x^{2}-2x)}dx
xy^'+y=11sqrt(x)	xy^{\prime\:}+y=11\sqrt{x}
derivative of x(6-x^{2/3})	\frac{d}{dx}(x(6-x)^{\frac{2}{3}})
integral of (sqrt(x^2-4))/(x^3)	\int\:\frac{\sqrt{x^{2}-4}}{x^{3}}dx
derivative of x^2e^2+2^y=5	\frac{d}{dx}(x^{2}e^{2}+2^{y})=5
area 4x^4-4x^2,x^2	area\:4x^{4}-4x^{2},x^{2}
derivative of sqrt((x-1/2))	\frac{d}{dx}(\sqrt{\frac{x-1}{2}})
derivative of (2x-3/((x^2+4)^2))	\frac{d}{dx}(\frac{2x-3}{(x^{2}+4)^{2}})
derivative of-x^2+4x+1	\frac{d}{dx}(-x^{2}+4x+1)
integral of ((4x^2+4))/((x^2-2x+2)^2)	\int\:\frac{(4x^{2}+4)}{(x^{2}-2x+2)^{2}}dx
derivative of (3+2xe^{-3x})	\frac{d}{dx}((3+2x)e^{-3x})
9y^{''}-12y^'+4y=0	9y^{\prime\:\prime\:}-12y^{\prime\:}+4y=0
tangent of (5x^2)/((3-4x)^4)	tangent\:\frac{5x^{2}}{(3-4x)^{4}}
laplacetransform sin(3t)cos(3t)	laplacetransform\:\sin(3t)\cos(3t)
tangent of f(x)= 1/(2sqrt(x)),\at x=1	tangent\:f(x)=\frac{1}{2\sqrt{x}},\at\:x=1
2y^{''}+11y^'-6y=0	2y^{\prime\:\prime\:}+11y^{\prime\:}-6y=0
(dy)/(dx)= y/(x^3+3x^2+2x)	\frac{dy}{dx}=\frac{y}{x^{3}+3x^{2}+2x}
f(x)=ln(1+sin(4/(x^2)))	f(x)=\ln(1+\sin(\frac{4}{x^{2}}))
tangent of y=sin(4x)+sin^2(4x),(0,0)	tangent\:y=\sin(4x)+\sin^{2}(4x),(0,0)
3ydx+2xdy=0	3ydx+2xdy=0
integral from 0 to infinity of e^{-4x}	\int\:_{0}^{\infty\:}e^{-4x}dx
f(x)=2xe^{2x}	f(x)=2xe^{2x}
integral of (32x^2)/((x-21)(x+7)^2)	\int\:\frac{32x^{2}}{(x-21)(x+7)^{2}}dx
slope of 2-3/x ,\at x=1	slope\:2-\frac{3}{x},\at\:x=1
derivative of \sqrt[5]{x^8}	\frac{d}{dx}(\sqrt[5]{x^{8}})
(\partial)/(\partial x)(ln(x+4y+2z))	\frac{\partial\:}{\partial\:x}(\ln(x+4y+2z))
integral from-2 to 3 of (x^2-3)	\int\:_{-2}^{3}(x^{2}-3)dx
derivative of sin(x+2y)	\frac{d}{dx}(\sin(x+2y))
y^'=2sqrt(y)	y^{\prime\:}=2\sqrt{y}
derivative of 1/(x^2+2)	\frac{d}{dx}(\frac{1}{x^{2}+2})
derivative of (7e^x+5e^{-x})/8	derivative\:\frac{7e^{x}+5e^{-x}}{8}
area 6x^2,x^2+12	area\:6x^{2},x^{2}+12
derivative of (x^9e^x/(x^9+e^x))	\frac{d}{dx}(\frac{x^{9}e^{x}}{x^{9}+e^{x}})
sum from n=1 to infinity of 2ne^{-n^2}	\sum\:_{n=1}^{\infty\:}2ne^{-n^{2}}
(y^3-2x^2y)dx+2x^3dy=0	(y^{3}-2x^{2}y)dx+2x^{3}dy=0
integral of x^3sqrt(x^2+7)	\int\:x^{3}\sqrt{x^{2}+7}dx
maclaurin cos(θ)	maclaurin\:\cos(θ)
(\partial)/(\partial x)(xln(y-z))	\frac{\partial\:}{\partial\:x}(x\ln(y-z))
limit as x approaches 2 of (x^2-4}{xcos(\frac{xpi)/2)-2cos((xpi)/2)}	\lim\:_{x\to\:2}(\frac{x^{2}-4}{x\cos(\frac{xπ}{2})-2\cos(\frac{xπ}{2})})
-2x^2y+y^'=-7x^2	-2x^{2}y+y^{\prime\:}=-7x^{2}
derivative of x(3x-4)^{0.5}	derivative\:x\cdot\:(3\cdot\:x-4)^{0.5}
(\partial)/(\partial y)(xz-5x^2y^3z^4)	\frac{\partial\:}{\partial\:y}(xz-5x^{2}y^{3}z^{4})
derivative of (-10x+4/(3x-8))	\frac{d}{dx}(\frac{-10x+4}{3x-8})
tangent of y=x^2+x	tangent\:y=x^{2}+x
integral of (x+y)	\int\:(x+y)dx
implicit (dy)/(dx),(3xy+7)^2=6y	implicit\:\frac{dy}{dx},(3xy+7)^{2}=6y
integral of sec^2(θ)tan^2(θ)	\int\:\sec^{2}(θ)\tan^{2}(θ)dθ
y^{''}+6sqrt(2)y^'+18y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+6\sqrt{2}y^{\prime\:}+18y=0,y(0)=1,y^{\prime\:}(0)=0
integral from-1 to 1 of sqrt(4-x^2)	\int\:_{-1}^{1}\sqrt{4-x^{2}}dx
(dy)/(dx)=x(e+y)	\frac{dy}{dx}=x(e+y)
derivative of y=-x^2	derivative\:y=-x^{2}
integral of cosh(x)	\int\:\cosh(x)dx
integral from 0 to x of ae^{-ax}	\int\:_{0}^{x}ae^{-ax}dx
derivative of 1/x-4x^2	\frac{d}{dx}(\frac{1}{x}-4x^{2})
area 2x^2+3,(-2,1)	area\:2x^{2}+3,(-2,1)
derivative of (x^3/x)	\frac{d}{dx}(\frac{x^{3}}{x})
limit as x approaches 0+of sin(3x)ln(x)	\lim\:_{x\to\:0+}(\sin(3x)\ln(x))
integral of 1/2 sqrt(u)	\int\:\frac{1}{2}\sqrt{u}du
integral from-7 to-3 of 1/x	\int\:_{-7}^{-3}\frac{1}{x}dx
integral of-e^xcos(y)	\int\:-e^{x}\cos(y)dy
(\partial)/(\partial x)(4x+6y+2z)	\frac{\partial\:}{\partial\:x}(4x+6y+2z)
y^{''}+2y^'+y=e^{-t}ln(t)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=e^{-t}\ln(t)
integral of 3/8 x^2	\int\:\frac{3}{8}x^{2}dx
(dy)/(dx)=(x+3y)/(y-3x)	\frac{dy}{dx}=\frac{x+3y}{y-3x}
integral of n^x	\int\:n^{x}dx
derivative of y=-25+5x+10e^{-x/5+1}	derivative\:y=-25+5x+10e^{-\frac{x}{5}+1}
y^'-7.5y=-12y^2	y^{\prime\:}-7.5y=-12y^{2}
(\partial)/(\partial y)(7e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:y}(7e^{yz}\cos(xyz))
derivative of x+sqrt(x)+7	\frac{d}{dx}(x+\sqrt{x}+7)
derivative of ((x+2(x^2-2x+4))/(x^3))	\frac{d}{dx}(\frac{(x+2)(x^{2}-2x+4)}{x^{3}})
integral of 1/(x^2sqrt(x^2-169))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-169}}dx
integral of (1-x^2)/(x^2)	\int\:\frac{1-x^{2}}{x^{2}}dx
y^{''}+4y^'+20y=80	y^{\prime\:\prime\:}+4y^{\prime\:}+20y=80
area y=sqrt(x),y=x-2,y=0	area\:y=\sqrt{x},y=x-2,y=0
integral of 1/((x^2+81)^2)	\int\:\frac{1}{(x^{2}+81)^{2}}dx
integral of 4cos^2(θ)	\int\:4\cos^{2}(θ)dθ
integral from 0 to 1/2 of tan(x/2)	\int\:_{0}^{\frac{1}{2}}\tan(\frac{x}{2})dx
limit as x approaches 0 of (2e^x-2)/x	\lim\:_{x\to\:0}(\frac{2e^{x}-2}{x})
(dy}{dt}= 1/10 ln(\frac{2000)/y)y	\frac{dy}{dt}=\frac{1}{10}\ln(\frac{2000}{y})y
integral of csc^2(1)	\int\:\csc^{2}(1)dx
f(x)=(x^3-1)/(2x+3)	f(x)=\frac{x^{3}-1}{2x+3}
derivative of (1+3x^2)(x-x^2)	derivative\:(1+3x^{2})(x-x^{2})
integral of \sqrt[3]{8x^7}	\int\:\sqrt[3]{8x^{7}}dx
limit as x approaches 2 of x^2-3x+5	\lim\:_{x\to\:2}(x^{2}-3x+5)
(4/x)^'	(\frac{4}{x})^{\prime\:}
integral of (e^x-e^{-x})/2	\int\:\frac{e^{x}-e^{-x}}{2}dx
integral of ((3+u))/(-(u^2-1))	\int\:\frac{(3+u)}{-(u^{2}-1)}du

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