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Popular Calculus Problems

integral of (x^2e^{2x}-3xe^{2x}+5e^{2x})	\int\:(x^{2}e^{2x}-3xe^{2x}+5e^{2x})dx
integral from 2 to 6 of 8	\int\:_{2}^{6}8dx
limit as x approaches 0 of 3sin(x)-1	\lim\:_{x\to\:0}(3\sin(x)-1)
derivative of (2x+5)/(sqrt(x))	derivative\:\frac{2x+5}{\sqrt{x}}
derivative of (x^3/({f)(x)})	\frac{d}{dx}(\frac{x^{3}}{{f}(x)})
integral of 9/(t^2)	\int\:\frac{9}{t^{2}}dt
integral of sec(θ)(sec(θ)+tan(θ))	\int\:\sec(θ)(\sec(θ)+\tan(θ))dθ
limit as x approaches 0 of x/(sin(12x))	\lim\:_{x\to\:0}(\frac{x}{\sin(12x)})
integral of (60)/(2x+5)-4	\int\:\frac{60}{2x+5}-4dx
integral from 1 to 8 of x^{-2/3}	\int\:_{1}^{8}x^{-\frac{2}{3}}dx
integral of (sqrt(36-x^2))/(x^2)	\int\:\frac{\sqrt{36-x^{2}}}{x^{2}}dx
derivative of f(x)=(x^23x)/6	derivative\:f(x)=\frac{x^{2}3x}{6}
integral of ae^{ax}(2+ax)	\int\:ae^{ax}(2+ax)dx
(dy)/(dx)=sin(19x)	\frac{dy}{dx}=\sin(19x)
integral from 4 to 5 of tsqrt(t-4)	\int\:_{4}^{5}t\sqrt{t-4}dt
derivative of y=6x-2	derivative\:y=6x-2
(\partial)/(\partial x)(arctan(x*sqrt(t)))	\frac{\partial\:}{\partial\:x}(\arctan(x\cdot\:\sqrt{t}))
laplacetransform 2^t	laplacetransform\:2^{t}
integral of ((e^{sqrt(x)}))/(sqrt(x))	\int\:\frac{(e^{\sqrt{x}})}{\sqrt{x}}dx
integral of e^{7x}sin(2x)	\int\:e^{7x}\sin(2x)dx
area 3x^2,3,-3,2	area\:3x^{2},3,-3,2
x^4-x+y-xy^'=0	x^{4}-x+y-xy^{\prime\:}=0
(\partial)/(\partial x)(e^{4x+5y})	\frac{\partial\:}{\partial\:x}(e^{4x+5y})
derivative of 1+3cos^2(x)	\frac{d}{dx}(1+3\cos^{2}(x))
integral of (2x-x^2-1)/(x^3+x)	\int\:\frac{2x-x^{2}-1}{x^{3}+x}dx
derivative of 7-5x	\frac{d}{dx}(7-5x)
tangent of y=arcsin(x/2),\at x=1	tangent\:y=\arcsin(\frac{x}{2}),\at\:x=1
(dx)/(dt)=sin(t)x+e^{-cos(t)}sin(t)	\frac{dx}{dt}=\sin(t)x+e^{-\cos(t)}\sin(t)
limit as x approaches infinity of-(5)	\lim\:_{x\to\:\infty\:}(-(5))
3y^'+sqrt(x)y=5sqrt(x),y(9)=4	3y^{\prime\:}+\sqrt{x}y=5\sqrt{x},y(9)=4
derivative of arctan(x)-arctan(x-7)	derivative\:\arctan(x)-\arctan(x-7)
3e^{4x}y^'=-16 x/(y^2),y(0)=1	3e^{4x}y^{\prime\:}=-16\frac{x}{y^{2}},y(0)=1
(\partial}{\partial y}(\frac{y^4)/x)	\frac{\partial\:}{\partial\:y}(\frac{y^{4}}{x})
d/(ds)(s+t)	\frac{d}{ds}(s+t)
limit as x approaches infinity of 538*x	\lim\:_{x\to\:\infty\:}(538\cdot\:x)
integral of x^4ln(4x)	\int\:x^{4}\ln(4x)dx
limit as x approaches-6-of 1/((x+6)^4)	\lim\:_{x\to\:-6-}(\frac{1}{(x+6)^{4}})
sum from n=0 to infinity of ln((n+1)/n)	\sum\:_{n=0}^{\infty\:}\ln(\frac{n+1}{n})
y^{''}+y=sin(2t)	y^{\prime\:\prime\:}+y=\sin(2t)
limit as x approaches 5 of-2x	\lim\:_{x\to\:5}(-2x)
derivative of f(x)=3x+2/x	derivative\:f(x)=3x+\frac{2}{x}
limit as x approaches 0 of 5-x/2	\lim\:_{x\to\:0}(5-\frac{x}{2})
limit as x approaches 8-of x/(x-8)	\lim\:_{x\to\:8-}(\frac{x}{x-8})
sum from n=1 to infinity of 4*3^n	\sum\:_{n=1}^{\infty\:}4\cdot\:3^{n}
integral of x/(x-4)	\int\:\frac{x}{x-4}dx
y^{'''}+8y=0	y^{\prime\:\prime\:\prime\:}+8y=0
d/(dt)(sqrt(6)t^2)	\frac{d}{dt}(\sqrt{6}t^{2})
derivative of (x+1^{2x})	\frac{d}{dx}((x+1)^{2x})
integral of (sec^2(2t))/(sqrt(5+3tan(2t)))	\int\:\frac{\sec^{2}(2t)}{\sqrt{5+3\tan(2t)}}dt
derivative of (x^2-3x/2)	\frac{d}{dx}(\frac{x^{2}-3x}{2})
tangent of f(x)=3x^2-x^3,\at x=1	tangent\:f(x)=3x^{2}-x^{3},\at\:x=1
derivative of-3sin(x-2)	\frac{d}{dx}(-3\sin(x)-2)
derivative of x-2ln(x)	\frac{d}{dx}(x-2\ln(x))
tangent of f(x)=11+9x-x^3,\at x=1	tangent\:f(x)=11+9x-x^{3},\at\:x=1
derivative of (\sqrt[3]{x}-3/(x-3))	\frac{d}{dx}(\frac{\sqrt[3]{x}-3}{x-3})
(\partial)/(\partial x)(1/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{(x-y)^{2}})
derivative of (10x^3-6x^2+3)/(4x^2-6x+3)	derivative\:\frac{10x^{3}-6x^{2}+3}{4x^{2}-6x+3}
limit as x approaches infinity of-1/3 ce^{-3(x)}	\lim\:_{x\to\:\infty\:}(-\frac{1}{3}ce^{-3(x)})
integral of (2/x-4e^x)	\int\:(\frac{2}{x}-4e^{x})dx
derivative of (1/(x^2)dx)	\frac{d}{dx}((\frac{1}{x^{2}})dx)
area sqrt(4x),x^2	area\:\sqrt{4x},x^{2}
(dy)/(dx)+y^5x+5y=0	\frac{dy}{dx}+y^{5}x+5y=0
derivative of y=(5x^3)/3-x+7e^x	derivative\:y=\frac{5x^{3}}{3}-x+7e^{x}
area-2x^3+23x^2-33x-108,[0,x]	area\:-2x^{3}+23x^{2}-33x-108,[0,x]
t(dy)/(dt)=2te^t-y+6t^2	t\frac{dy}{dt}=2te^{t}-y+6t^{2}
integral of 2e^6	\int\:2e^{6}dx
integral of sqrt(1)+sqrt(x)	\int\:\sqrt{1}+\sqrt{x}dx
limit as x approaches 8 of x/(x^2-64)	\lim\:_{x\to\:8}(\frac{x}{x^{2}-64})
x(dy)/(dx)+y^2+y=0	x\frac{dy}{dx}+y^{2}+y=0
derivative of sqrt(9x+x^2)	\frac{d}{dx}(\sqrt{9x+x^{2}})
integral of (sin(5x))/(e^{cos(5x)-1)}	\int\:\frac{\sin(5x)}{e^{\cos(5x)-1}}dx
derivative of (-1/((x+2)^2))	\frac{d}{dx}(\frac{-1}{(x+2)^{2}})
taylor xe^{-x+1}1	taylor\:xe^{-x+1}1
slope of (81)(8-7)	slope\:(81)(8-7)
area y=12-7x-x^2,y=4	area\:y=12-7x-x^{2},y=4
implicit cos(yx^3)= 1/6	implicit\:\cos(yx^{3})=\frac{1}{6}
integral of (3/x+4/(x^5))	\int\:(\frac{3}{x}+\frac{4}{x^{5}})dx
y=(x^2)/(sqrt(x))	y=\frac{x^{2}}{\sqrt{x}}
integral of 1/x-2/(x^2)+5/(x^3)	\int\:\frac{1}{x}-\frac{2}{x^{2}}+\frac{5}{x^{3}}dx
d/(dt)({z}(t))	\frac{d}{dt}({z}(t))
derivative of f(x)=x^2e^x-2xe^x+4e^x	derivative\:f(x)=x^{2}e^{x}-2xe^{x}+4e^{x}
integral of-2xcos(x)	\int\:-2x\cos(x)dx
y^{''}= 6/(x^4)	y^{\prime\:\prime\:}=\frac{6}{x^{4}}
derivative of sqrt(x+15)	\frac{d}{dx}(\sqrt{x+15})
slope of (sqrt(3x+1))(8.5)	slope\:(\sqrt{3x+1})(8.5)
integral from-1 to 2 of x+2	\int\:_{-1}^{2}x+2dx
area y= 3/x ,y=12x,y= 1/(12x)	area\:y=\frac{3}{x},y=12x,y=\frac{1}{12x}
integral of (2x)/(x^2+4x+12)	\int\:\frac{2x}{x^{2}+4x+12}dx
integral of (cos(x))/(1+sin^2(x))	\int\:\frac{\cos(x)}{1+\sin^{2}(x)}dx
derivative of-9cot(xcsc(x))	\frac{d}{dx}(-9\cot(x)\csc(x))
derivative of ln((3+e^x/(3-e^x)))	\frac{d}{dx}(\ln(\frac{3+e^{x}}{3-e^{x}}))
derivative of ax^4+bx^3+cx^2	\frac{d}{dx}(ax^{4}+bx^{3}+cx^{2})
derivative of (3x-1)^7(2x+1)^5	derivative\:(3x-1)^{7}(2x+1)^{5}
d/(dy)(e^{2y})	\frac{d}{dy}(e^{2y})
derivative of f(x)=x^6(x-1)^5	derivative\:f(x)=x^{6}(x-1)^{5}
integral of (x^4-1/2 x^3+1/4 x-2)	\int\:(x^{4}-\frac{1}{2}x^{3}+\frac{1}{4}x-2)dx
sum from n=1 to infinity of ((4pi)/5)^n	\sum\:_{n=1}^{\infty\:}(\frac{4π}{5})^{n}
integral of x^2+x-3	\int\:x^{2}+x-3dx
derivative of sin(4x+sin^2(4x))	\frac{d}{dx}(\sin(4x)+\sin^{2}(4x))
y^{''}+3y^'+2y=e^{-t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{-t},y(0)=0,y^{\prime\:}(0)=0

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