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Popular Calculus Problems

integral from 5 to 6 of x/(x^2+6x+13)	\int\:_{5}^{6}\frac{x}{x^{2}+6x+13}dx
derivative of e^{ax}sin(bx)	derivative\:e^{ax}\sin(bx)
limit as x approaches 3 of e^{2/(3-x)}	\lim\:_{x\to\:3}(e^{\frac{2}{3-x}})
(\partial)/(\partial y)(e^{2x}cos(y))	\frac{\partial\:}{\partial\:y}(e^{2x}\cos(y))
integral of e^{-x}cos^2(x)	\int\:e^{-x}\cos^{2}(x)dx
integral of (xsqrt(9-x^2))	\int\:(x\sqrt{9-x^{2}})dx
(dy)/(dx)=e^{2y+2x}	\frac{dy}{dx}=e^{2y+2x}
derivative of x-3x^2	\frac{d}{dx}(x-3x^{2})
4x^2y^2dx+x^3ydy=0	4x^{2}y^{2}dx+x^{3}ydy=0
integral from-3 to 3 of (sqrt(9-x^2))^2	\int\:_{-3}^{3}(\sqrt{9-x^{2}})^{2}dx
integral of e^{-2x}(x^2+5)	\int\:e^{-2x}(x^{2}+5)dx
y^{''}-6y^'+12y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+12y=0
derivative of 20sqrt(x)	derivative\:20\sqrt{x}
taylor e^{x-1}	taylor\:e^{x-1}
derivative of (3xy/(x^2+y^2))	\frac{d}{dx}(\frac{3xy}{x^{2}+y^{2}})
y^{'''}+2y^{''}+y^'+2y=0	y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}+y^{\prime\:}+2y=0
limit as n approaches infinity of n^{-2}	\lim\:_{n\to\:\infty\:}(n^{-2})
area 2,sqrt(x),x^2	area\:2,\sqrt{x},x^{2}
derivative of (x^3^{1/2})	\frac{d}{dx}((x^{3})^{\frac{1}{2}})
derivative of y=sqrt(ln(x))	derivative\:y=\sqrt{\ln(x)}
area y=x^2-4x,y=-x^2	area\:y=x^{2}-4x,y=-x^{2}
integral of x^2-3x-4	\int\:x^{2}-3x-4dx
limit as x approaches-2+of x/(x^2-3x-10)	\lim\:_{x\to\:-2+}(\frac{x}{x^{2}-3x-10})
derivative of y= x/(10)-(10)/x	derivative\:y=\frac{x}{10}-\frac{10}{x}
integral of ((cos^2(at)))/a	\int\:\frac{(\cos^{2}(at))}{a}dx
implicit (dy)/(dx),(7xy+5)^2=42y	implicit\:\frac{dy}{dx},(7xy+5)^{2}=42y
derivative of (7x^6+4x^3^4)	\frac{d}{dx}((7x^{6}+4x^{3})^{4})
derivative of x/((5x-4^3))	\frac{d}{dx}(\frac{x}{(5x-4)^{3}})
integral of arccot(2x)	\int\:\arccot(2x)dx
limit as t approaches 0 of ((2e^t-2))/t	\lim\:_{t\to\:0}(\frac{(2e^{t}-2)}{t})
derivative of e^xsqrt(x)	derivative\:e^{x}\sqrt{x}
limit as x approaches 0+of (-2x^4-14x)/x	\lim\:_{x\to\:0+}(\frac{-2x^{4}-14x}{x})
integral of tsin(2t)	\int\:t\sin(2t)dt
limit as x approaches 0+of x^2sin(1/x)	\lim\:_{x\to\:0+}(x^{2}\sin(\frac{1}{x}))
(\partial)/(\partial y)(4y^3-100y)	\frac{\partial\:}{\partial\:y}(4y^{3}-100y)
integral from 1 to 3 of 2\sqrt[4]{x^3}	\int\:_{1}^{3}2\sqrt[4]{x^{3}}dx
y^'=(1+x)(1+y^2)	y^{\prime\:}=(1+x)(1+y^{2})
integral of e^{(-2x)}	\int\:e^{(-2x)}dx
integral from-1 to 2 of (y+2)-y^2	\int\:_{-1}^{2}(y+2)-y^{2}dy
integral of xye^{xz}	\int\:xye^{xz}dz
(\partial)/(\partial z)(e^{cos(x^2)})	\frac{\partial\:}{\partial\:z}(e^{\cos(x^{2})})
integral of 1/(sqrt(9-16t^2))	\int\:\frac{1}{\sqrt{9-16t^{2}}}dt
derivative of (4x)/(sqrt(x^2+4))	derivative\:\frac{4x}{\sqrt{x^{2}+4}}
limit as x approaches 2+of ln(x-2)	\lim\:_{x\to\:2+}(\ln(x-2))
integral of sqrt(48+2x-x^2)	\int\:\sqrt{48+2x-x^{2}}dx
derivative of y+x	\frac{d}{dx}(y+x)
limit as x approaches 0 of 5x^3+2x	\lim\:_{x\to\:0}(5x^{3}+2x)
e^xy(dy)/(dx)=e^{-y}+e^{-6x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-6x-y}
integral of 1/(sqrt((x-1)^2-4))	\int\:\frac{1}{\sqrt{(x-1)^{2}-4}}dx
derivative of 6xln(x+5x)	\frac{d}{dx}(6x\ln(x)+5x)
tangent of f(x)=2x^4-4x^2+6,\at x=-2	tangent\:f(x)=2x^{4}-4x^{2}+6,\at\:x=-2
(\partial)/(\partial z)(tan(1+2x^2y^3z^2))	\frac{\partial\:}{\partial\:z}(\tan(1+2x^{2}y^{3}z^{2}))
integral from-pi to pi of e^{-inx}	\int\:_{-π}^{π}e^{-inx}dx
derivative of f(x)= 4/(sqrt(x))	derivative\:f(x)=\frac{4}{\sqrt{x}}
derivative of (3x(4-x)/(5x^2))	\frac{d}{dx}(\frac{3x(4-x)}{5x^{2}})
limit as x approaches 0 of (sin(3x))/x+2	\lim\:_{x\to\:0}(\frac{\sin(3x)}{x}+2)
1/(x^4)(dy)/(dx)=19+15y	\frac{1}{x^{4}}\frac{dy}{dx}=19+15y
(d^2)/(dx^2)(t^3(e)^{3t})	\frac{d^{2}}{dx^{2}}(t^{3}(e)^{3t})
integral of (t^2+1)e^{-2t}	\int\:(t^{2}+1)e^{-2t}dt
tangent of y=4sin(x)cos(x),\at x= pi/4	tangent\:y=4\sin(x)\cos(x),\at\:x=\frac{π}{4}
implicit 4x^2+4x+xy=4	implicit\:4x^{2}+4x+xy=4
limit as n approaches infinity of 1000(1.06)^n	\lim\:_{n\to\:\infty\:}(1000(1.06)^{n})
y^{''}+y=0,y(pi/3)=4,y^'(pi/3)=-8	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=4,y^{\prime\:}(\frac{π}{3})=-8
area e^x,e^{-4x},[0,ln(4)]	area\:e^{x},e^{-4x},[0,\ln(4)]
tangent of f(x)=5x^3-5x,\at x=1	tangent\:f(x)=5x^{3}-5x,\at\:x=1
derivative of e^{3-x^2}	\frac{d}{dx}(e^{3-x^{2}})
sum from n=4 to infinity of 1/(n^{3/2)}	\sum\:_{n=4}^{\infty\:}\frac{1}{n^{\frac{3}{2}}}
integral of x/((2-x^2)^2)	\int\:\frac{x}{(2-x^{2})^{2}}dx
y^'=((6x^4+y^4))/(xy^3)	y^{\prime\:}=\frac{(6x^{4}+y^{4})}{xy^{3}}
integral from 0 to pi/2 of 18cos^5(x)	\int\:_{0}^{\frac{π}{2}}18\cos^{5}(x)dx
integral of (e^{3/x})/(x^2)	\int\:\frac{e^{\frac{3}{x}}}{x^{2}}dx
integral of (x^3+3)^2(3x)	\int\:(x^{3}+3)^{2}(3x)dx
integral of (2x+1)/(x^2+2x+50)	\int\:\frac{2x+1}{x^{2}+2x+50}dx
integral of 1/(xsqrt(16x^2+1))	\int\:\frac{1}{x\sqrt{16x^{2}+1}}dx
implicit (dy)/(dx),ln(y)=x	implicit\:\frac{dy}{dx},\ln(y)=x
integral of y/1	\int\:\frac{y}{1}dy
taylor x^{(1/3)}	taylor\:x^{(\frac{1}{3})}
integral of 1/(1-v^2)	\int\:\frac{1}{1-v^{2}}dv
d/(dt)(1-\|t\|)	\frac{d}{dt}(1-\left\|t\right\|)
integral of-sin(x)-e^{-x}+3x^2	\int\:-\sin(x)-e^{-x}+3x^{2}dx
y^{''}+5y^'+4y=8x^2+e^{-x}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=8x^{2}+e^{-x}
(dy)/(dx)=2x(y-1)	\frac{dy}{dx}=2x(y-1)
integral of (sqrt(7-x^4))/(5x)	\int\:\frac{\sqrt{7-x^{4}}}{5x}dx
derivative of 7x-2y	derivative\:7x-2y
(dy)/(dx)=xy^{1/2}	\frac{dy}{dx}=xy^{\frac{1}{2}}
limit as x approaches-3 of (x^2+3)/4	\lim\:_{x\to\:-3}(\frac{x^{2}+3}{4})
limit as x approaches 1 of e	\lim\:_{x\to\:1}(e)
sum from n=1 to infinity of (1/3)^{k-n}	\sum\:_{n=1}^{\infty\:}(\frac{1}{3})^{k-n}
derivative of 5sec^2(x)	derivative\:5\sec^{2}(x)
sum from k=1 to infinity of (x^k)/k	\sum\:_{k=1}^{\infty\:}\frac{x^{k}}{k}
f(x)=sec(x)tan(x)	f(x)=\sec(x)\tan(x)
area x^2-2x,2x-3	area\:x^{2}-2x,2x-3
integral from 0 to 1 of (93)/(x^5)	\int\:_{0}^{1}\frac{93}{x^{5}}dx
integral of (x^{1.3}+9x^{3.5})	\int\:(x^{1.3}+9x^{3.5})dx
integral of 5/((x-3)(x+2))	\int\:\frac{5}{(x-3)(x+2)}dx
derivative of (4x/(1-cot(x)))	\frac{d}{dx}(\frac{4x}{1-\cot(x)})
derivative of 2/(4-x)	derivative\:\frac{2}{4-x}
derivative of x-pi	\frac{d}{dx}(x-π)
tangent of y= 1/(x^4),(-2, 1/16)	tangent\:y=\frac{1}{x^{4}},(-2,\frac{1}{16})
integral of (2e^x)	\int\:(2e^{x})dx

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