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Popular Calculus Problems

derivative of 1+ln(x)	\frac{d}{dx}(1+\ln(x))
sum from i=1 to infinity of 3(1/4)^{i-1}	\sum\:_{i=1}^{\infty\:}3(\frac{1}{4})^{i-1}
limit as x approaches 1 of (in(x))/(x-1)	\lim\:_{x\to\:1}(\frac{in(x)}{x-1})
derivative of y=sqrt(x^2+10x)	derivative\:y=\sqrt{x^{2}+10x}
(dy}{dx}=\frac{x^2-2y)/x ,y(2)=2	\frac{dy}{dx}=\frac{x^{2}-2y}{x},y(2)=2
derivative of 5(2^x)	derivative\:5(2^{x})
integral from pi/6 to pi/2 of cot(x)	\int\:_{\frac{π}{6}}^{\frac{π}{2}}\cot(x)dx
integral of pixcos(nx)	\int\:πx\cos(nx)dx
derivative of 2x^{4/3}-3x^{2/3}	\frac{d}{dx}(2x^{\frac{4}{3}}-3x^{\frac{2}{3}})
derivative of-(e^{1/x}/(x^2))	\frac{d}{dx}(-\frac{e^{\frac{1}{x}}}{x^{2}})
integral of 2cos^3(x)	\int\:2\cos^{3}(x)dx
integral of (2x-1/(8x))^2	\int\:(2x-\frac{1}{8x})^{2}dx
derivative of (x^3/9+3/(4x))	\frac{d}{dx}(\frac{x^{3}}{9}+\frac{3}{4x})
area 9(x^3-x),0	area\:9(x^{3}-x),0
integral of y^2\sqrt[5]{2-4y^3}	\int\:y^{2}\sqrt[5]{2-4y^{3}}dy
slope of (-3/4 , 1/4),(1/2 ,-3/2)	slope\:(-\frac{3}{4},\frac{1}{4}),(\frac{1}{2},-\frac{3}{2})
area f(x)=x^2-4,g(x)=0,x=-4,x=3	area\:f(x)=x^{2}-4,g(x)=0,x=-4,x=3
(\partial)/(\partial y)(sqrt(25-x^2-5y))	\frac{\partial\:}{\partial\:y}(\sqrt{25-x^{2}-5y})
integral of 6xsqrt(1+x^2)	\int\:6x\sqrt{1+x^{2}}dx
y^{''}+20y^'+500y=0	y^{\prime\:\prime\:}+20y^{\prime\:}+500y=0
xdy+ydx=0	xdy+ydx=0
integral of pit-t^2cos(nt)	\int\:πt-t^{2}\cos(nt)dt
inverse oflaplace (2/3)/(s^2+2s+17)	inverselaplace\:\frac{\frac{2}{3}}{s^{2}+2s+17}
integral of (tan(5x)-sec(5x))^2	\int\:(\tan(5x)-\sec(5x))^{2}dx
(dy)/(dx)=y^2e^xsin(3x)	\frac{dy}{dx}=y^{2}e^{x}\sin(3x)
integral of sin(3t)	\int\:\sin(3t)dt
integral from 0 to 5 of x 2/95 (12-x)	\int\:_{0}^{5}x\frac{2}{95}(12-x)dx
derivative of (sqrt(x)/(1+x^2))	\frac{d}{dx}(\frac{\sqrt{x}}{1+x^{2}})
tangent of y= 8/(sqrt(x)),(16, 8/4)	tangent\:y=\frac{8}{\sqrt{x}},(16,\frac{8}{4})
integral from 0 to 1 of 5(1+sqrt(x))^6	\int\:_{0}^{1}5(1+\sqrt{x})^{6}dx
limit as x approaches-4 of 3x^2-4x+8	\lim\:_{x\to\:-4}(3x^{2}-4x+8)
area cos(x),2-cos(x),[0,2pi]	area\:\cos(x),2-\cos(x),[0,2π]
derivative of-16t^2+44t+31	derivative\:-16t^{2}+44t+31
limit as x approaches 2 of 3x-5	\lim\:_{x\to\:2}(3x-5)
derivative of (1-ln(x)/(x^2))	\frac{d}{dx}(\frac{1-\ln(x)}{x^{2}})
derivative of-(50/(x^2))	\frac{d}{dx}(-\frac{50}{x^{2}})
integral of 1/((x^2-1)^2)	\int\:\frac{1}{(x^{2}-1)^{2}}dx
(\partial)/(\partial y)(7x^{4y})	\frac{\partial\:}{\partial\:y}(7x^{4y})
derivative of x^{-2}e^x	\frac{d}{dx}(x^{-2}e^{x})
(dy)/(dx)=y^2*x^{-3}	\frac{dy}{dx}=y^{2}\cdot\:x^{-3}
integral of 9xe^{-4x}	\int\:9xe^{-4x}dx
integral of (3xz^2+2)	\int\:(3xz^{2}+2)dz
derivative of log_{10}((x^2-1/x))	\frac{d}{dx}(\log_{10}(\frac{x^{2}-1}{x}))
integral of (ln(x))(sin(x))	\int\:(\ln(x))(\sin(x))dx
(dr)/(dθ)cot(θ)-r=2	\frac{dr}{dθ}\cot(θ)-r=2
integral from 1 to 4 of-8sqrt(t)ln(t)	\int\:_{1}^{4}-8\sqrt{t}\ln(t)dt
integral of 1/(x^3)sqrt((x^2-1)/(x^2))	\int\:\frac{1}{x^{3}}\sqrt{\frac{x^{2}-1}{x^{2}}}dx
taylor x-1	taylor\:x-1
tangent of (-1)/((2x+1)sqrt(2x+1))	tangent\:\frac{-1}{(2x+1)\sqrt{2x+1}}
derivative of e^{8-x}	\frac{d}{dx}(e^{8-x})
derivative of sqrt(x^2+1)+x^2	derivative\:\sqrt{x^{2}+1}+x^{2}
integral of (2t-1)^2	\int\:(2t-1)^{2}dt
derivative of 3*cos(x)	\frac{d}{dx}(3\cdot\:\cos(x))
derivative of (sqrt(3x^2)/2)	\frac{d}{dx}(\frac{\sqrt{3x^{2}}}{2})
derivative of 5ln(12x)	\frac{d}{dx}(5\ln(12x))
(dy)/(dx)-2y=x	\frac{dy}{dx}-2y=x
derivative of 6x+7	\frac{d}{dx}(6x+7)
integral of ((1+t)/t)^3	\int\:(\frac{1+t}{t})^{3}dt
integral of xabe^{-abx+abc}	\int\:x\cdot\:ab\cdot\:e^{-abx+abc}dx
derivative of x+(100/x)	\frac{d}{dx}(x+\frac{100}{x})
(2y^2+4x^2)dx-xydy=0	(2y^{2}+4x^{2})dx-xydy=0
derivative of cos(5x-3)	\frac{d}{dx}(\cos(5x-3))
integral of e^{-0.12x}	\int\:e^{-0.12x}dx
integral of 1/(z^2)	\int\:\frac{1}{z^{2}}dz
derivative of f(x)=-5e^{-5x+2}	derivative\:f(x)=-5e^{-5x+2}
derivative of f(x)= x/(7-sqrt(x))	derivative\:f(x)=\frac{x}{7-\sqrt{x}}
derivative of arctan(ax)	\frac{d}{dx}(\arctan(ax))
derivative of (x^3/6+1/(2x))	\frac{d}{dx}(\frac{x^{3}}{6}+\frac{1}{2x})
derivative of f(x)=-21x-3	derivative\:f(x)=-21x-3
(\partial)/(\partial y)(0.5x^2+y^2-3x+2y-5)	\frac{\partial\:}{\partial\:y}(0.5x^{2}+y^{2}-3x+2y-5)
derivative of ln(ax+b)	\frac{d}{dx}(\ln(ax+b))
x*(dy)/(dx)+2y=3x	x\cdot\:\frac{dy}{dx}+2y=3x
integral of 1/(1+cosh(x))	\int\:\frac{1}{1+\cosh(x)}dx
(\partial)/(\partial y)(5x^3y^6)	\frac{\partial\:}{\partial\:y}(5x^{3}y^{6})
(y^'+0.3334y)/((20.004x+6000))=20	\frac{y^{\prime\:}+0.3334y}{(20.004x+6000)}=20
inverse oflaplace (1-3s)/(s^2+8s+21)	inverselaplace\:\frac{1-3s}{s^{2}+8s+21}
integral of (x^2)/(sqrt(x^3+3600))	\int\:\frac{x^{2}}{\sqrt{x^{3}+3600}}dx
laplacetransform te^{6t}sin(3t)	laplacetransform\:te^{6t}\sin(3t)
laplacetransform e^t*cos(t)	laplacetransform\:e^{t}\cdot\:\cos(t)
(5y-2x)((dy)/(dx))-2y=0	(5y-2x)(\frac{dy}{dx})-2y=0
slope ofintercept (5)(0.5)	slopeintercept\:(5)(0.5)
area y=x^2-7,y=2	area\:y=x^{2}-7,y=2
limit as x approaches 2 of-x^3+2x^2-1	\lim\:_{x\to\:2}(-x^{3}+2x^{2}-1)
integral of (x^2)/((144+x^2)^2)	\int\:\frac{x^{2}}{(144+x^{2})^{2}}dx
limit as x approaches 0 of arctan(5/x)	\lim\:_{x\to\:0}(\arctan(\frac{5}{x}))
integral of 6cos(x)	\int\:6\cos(x)dx
-6y^{''}+54y^'=0,y(2)=1,y^'(-1)=1	-6y^{\prime\:\prime\:}+54y^{\prime\:}=0,y(2)=1,y^{\prime\:}(-1)=1
integral from 0 to 1 of 3x	\int\:_{0}^{1}3xdx
(dy)/(dx)= 2/(sqrt(16-x^2))	\frac{dy}{dx}=\frac{2}{\sqrt{16-x^{2}}}
derivative of sec(3x)	derivative\:\sec(3x)
integral of 1/(θ^2)cos(1/θ)	\int\:\frac{1}{θ^{2}}\cos(\frac{1}{θ})dθ
(\partial)/(\partial x)(e^{sin(2x)})	\frac{\partial\:}{\partial\:x}(e^{\sin(2x)})
(dy)/(dx)=-(5y)/(50+x)	\frac{dy}{dx}=-\frac{5y}{50+x}
xy^'=5y-x,y(1)=1	xy^{\prime\:}=5y-x,y(1)=1
integral of (arccos(sqrt(x)))/(sqrt(x))	\int\:\frac{\arccos(\sqrt{x})}{\sqrt{x}}dx
integral of 4xln(3x)	\int\:4x\ln(3x)dx
integral of ye^{ty}	\int\:ye^{ty}
integral of 6/(sqrt(10x-x^2))	\int\:\frac{6}{\sqrt{10x-x^{2}}}dx
derivative of x^2+(128/x)	\frac{d}{dx}(x^{2}+\frac{128}{x})
derivative of f(x)=sin(arccos(x))	derivative\:f(x)=\sin(\arccos(x))

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