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Popular Calculus Problems

inverse oflaplace 1/(s^2+2pis+pi^2)	inverselaplace\:\frac{1}{s^{2}+2\cdot\:π\cdot\:s+π^{2}}
sum from n=3 to infinity of e^{5-6n}	\sum\:_{n=3}^{\infty\:}e^{5-6n}
(d^2y)/(dx^2)-(dy)/(dx)-2y=0	\frac{d^{2}y}{dx^{2}}-\frac{dy}{dx}-2y=0
derivative of tan(x)-1sec(x)	derivative\:\tan(x)-1\sec(x)
integral of sqrt(y^2+1)	\int\:\sqrt{y^{2}+1}dy
tangent of y=sin(sin(x)),\at x=pi	tangent\:y=\sin(\sin(x)),\at\:x=π
integral of (\sqrt[10]{x})	\int\:(\sqrt[10]{x})dx
normal of y=sqrt(x),(9,3)	normal\:y=\sqrt{x},(9,3)
derivative of (sin(x)+cos(x))/(cos(x))	derivative\:\frac{\sin(x)+\cos(x)}{\cos(x)}
tangent of y=(8x)/(x^2+1),(-1,-4)	tangent\:y=\frac{8x}{x^{2}+1},(-1,-4)
integral of 1/(sqrt(x^2+2x-24))	\int\:\frac{1}{\sqrt{x^{2}+2x-24}}dx
(\partial)/(\partial y)(((x^2y))/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{(x^{2}y)}{x^{2}+y^{2}})
slope of 6x^2+2xy+2y^2=74,(3,2)	slope\:6x^{2}+2xy+2y^{2}=74,(3,2)
f(t)=\sqrt[3]{t}	f(t)=\sqrt[3]{t}
integral of 1/(sqrt(1-36x^2))	\int\:\frac{1}{\sqrt{1-36x^{2}}}dx
y^{'''}-4y^{''}-y^'+4y=0	y^{\prime\:\prime\:\prime\:}-4y^{\prime\:\prime\:}-y^{\prime\:}+4y=0
limit as x approaches 2 of (3^x-9)/(x-2)	\lim\:_{x\to\:2}(\frac{3^{x}-9}{x-2})
(\partial)/(\partial x)(9xe^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(9xe^{x^{2}+y^{2}})
derivative of 1/5 x^5-2x^3+3x	\frac{d}{dx}(\frac{1}{5}x^{5}-2x^{3}+3x)
limit as x approaches-1 of 6x+3	\lim\:_{x\to\:-1}(6x+3)
limit as x approaches 1 of (e^x)/(1-x)	\lim\:_{x\to\:1}(\frac{e^{x}}{1-x})
limit as x approaches 1 of (1(x))/(1-\sqrt[3]{x)}	\lim\:_{x\to\:1}(\frac{1(x)}{1-\sqrt[3]{x}})
limit as s approaches 0 of 1/s	\lim\:_{s\to\:0}(\frac{1}{s})
integral from 0 to 1 of 2pi(2-y)(7y^2)	\int\:_{0}^{1}2π(2-y)(7y^{2})dy
area x=49-y^2,x=y^2-49	area\:x=49-y^{2},x=y^{2}-49
limit as x approaches 0 of log_{5}(3x)	\lim\:_{x\to\:0}(\log_{5}(3x))
derivative of e^{x^2-4}+5x+6	\frac{d}{dx}(e^{x^{2}-4}+5x+6)
derivative of sin(\sqrt[3]{x})+\sqrt[3]{sin(3x)}	derivative\:\sin(\sqrt[3]{x})+\sqrt[3]{\sin(3x)}
integral of (cos(x))/(7+sin(x))	\int\:\frac{\cos(x)}{7+\sin(x)}dx
integral from-6 to 6 of 3t+4e^{2t}-e^t	\int\:_{-6}^{6}3t+4e^{2t}-e^{t}dt
(\partial)/(\partial y)(xyz+sin(2xy))	\frac{\partial\:}{\partial\:y}(xyz+\sin(2xy))
area 5cos(pix),12x^3-3,0.5,-0.5	area\:5\cos(πx),12x^{3}-3,0.5,-0.5
taylor 1/(1+x),1	taylor\:\frac{1}{1+x},1
area f(x)=x^3-6x,g(x)=-2x	area\:f(x)=x^{3}-6x,g(x)=-2x
derivative of 36t^2	derivative\:36t^{2}
integral of x^2sqrt(3x+6)	\int\:x^{2}\sqrt{3x+6}dx
integral of ((y^4+2y^2-1)/(sqrt(y)))	\int\:(\frac{y^{4}+2y^{2}-1}{\sqrt{y}})dy
(\partial)/(\partial z)(xyz+xy^4+yz^4+zx^4)	\frac{\partial\:}{\partial\:z}(xyz+xy^{4}+yz^{4}+zx^{4})
(\partial)/(\partial z)(xsin(y))	\frac{\partial\:}{\partial\:z}(x\sin(y))
integral from 0 to 2 of sin((pit)/2)	\int\:_{0}^{2}\sin(\frac{πt}{2})dt
integral of 18t^8e^{-t^9}	\int\:18t^{8}e^{-t^{9}}dt
(\partial}{\partial z}(xysin(\frac{piz)/3))	\frac{\partial\:}{\partial\:z}(xy\sin(\frac{πz}{3}))
(\partial)/(\partial x)(xe^y-3yz)	\frac{\partial\:}{\partial\:x}(xe^{y}-3yz)
derivative of 3/((x-1)^2)	derivative\:\frac{3}{(x-1)^{2}}
tangent of (x^2)/(x+2)	tangent\:\frac{x^{2}}{x+2}
derivative of Ax^2+Bx	\frac{d}{dx}(Ax^{2}+Bx)
integral of cos(5x)sin(6x)	\int\:\cos(5x)\sin(6x)dx
integral of xsqrt(x+3)	\int\:x\sqrt{x+3}dx
(dy)/(dx)=((x+3y))/(y-3x)	\frac{dy}{dx}=\frac{(x+3y)}{y-3x}
limit as x approaches 3 of (x^3-6x^2+9)/(x^2-9)	\lim\:_{x\to\:3}(\frac{x^{3}-6x^{2}+9}{x^{2}-9})
tangent of y=7x-4x^2,(-3,-57)	tangent\:y=7x-4x^{2},(-3,-57)
limit as x approaches 999 of x^2-1	\lim\:_{x\to\:999}(x^{2}-1)
integral of (4x)/(1-2x)	\int\:\frac{4x}{1-2x}dx
inverse oflaplace (s+4)/(s^2+4s+8)	inverselaplace\:\frac{s+4}{s^{2}+4s+8}
(dy)/(dx)=2xy,y(0)=1	\frac{dy}{dx}=2xy,y(0)=1
derivative of (t^3)/3	derivative\:\frac{t^{3}}{3}
tangent of f(x)= 1/(x^4),(-3, 1/81)	tangent\:f(x)=\frac{1}{x^{4}},(-3,\frac{1}{81})
taylor 1/(1-x),12	taylor\:\frac{1}{1-x},12
integral of (2x^3)/(x^2-4)	\int\:\frac{2x^{3}}{x^{2}-4}dx
derivative of \|x-3\|-\|2x-2\|-1xe[-2,2]	\frac{d}{dx}(\left\|x-3\right\|-\left\|2x-2\right\|-1xe[-2,2])
derivative of 1+xln(xy-5)	\frac{d}{dx}(1+x\ln(xy-5))
y^{'''}+y^'=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=0
limit as x approaches 2 of 3x^2+2x-1	\lim\:_{x\to\:2}(3x^{2}+2x-1)
integral of 1/(sqrt(x^2+a))	\int\:\frac{1}{\sqrt{x^{2}+a}}dx
integral of (y^4+y^2-1)/(y^3+y)	\int\:\frac{y^{4}+y^{2}-1}{y^{3}+y}dy
sum from n=0 to infinity of 5/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{5}{2^{n}}
inverse oflaplace 5/((s-2)(s-3)(s-6))	inverselaplace\:\frac{5}{(s-2)(s-3)(s-6)}
integral of cot(θ/5)	\int\:\cot(\frac{θ}{5})dθ
integral of (48x^2)/((x-24)(x+8)^2)	\int\:\frac{48x^{2}}{(x-24)(x+8)^{2}}dx
integral from 7 to infinity of e^{-2x}+x^{-3}	\int\:_{7}^{\infty\:}e^{-2x}+x^{-3}dx
tangent of x^3+y^3-9xy=0,(2,4)	tangent\:x^{3}+y^{3}-9xy=0,(2,4)
y^'=y^2x	y^{\prime\:}=y^{2}x
limit as x approaches pi/4 of 3cos(x)	\lim\:_{x\to\:\frac{π}{4}}(3\cos(x))
derivative of x(8-x^{1/3})	\frac{d}{dx}(x(8-x)^{\frac{1}{3}})
derivative of \sqrt[5]{2x^3+8x}	derivative\:\sqrt[5]{2x^{3}+8x}
integral of-3e^{-3t}	\int\:-3e^{-3t}dt
(\partial)/(\partial x)(\|x\|)	\frac{\partial\:}{\partial\:x}(\left\|x\right\|)
integral from-8 to 10 of (x+10)	\int\:_{-8}^{10}(x+10)dx
derivative of 2pix	\frac{d}{dx}(2πx)
integral of (x+2)/(x^2+9x-10)	\int\:\frac{x+2}{x^{2}+9x-10}dx
area y=8x^4-8x^2,y=9x^2	area\:y=8x^{4}-8x^{2},y=9x^{2}
derivative of 3(2xcos(5x)-5x^2sin(5x))	derivative\:3(2x\cos(5x)-5x^{2}\sin(5x))
slope of (0.2)(5.4)	slope\:(0.2)(5.4)
(\partial)/(\partial x)(sqrt(u^7+v^7))	\frac{\partial\:}{\partial\:x}(\sqrt{u^{7}+v^{7}})
derivative of (1+x^{1/x})	\frac{d}{dx}((1+x)^{\frac{1}{x}})
integral from 0 to pi/2 of cos^9(x)	\int\:_{0}^{\frac{π}{2}}\cos^{9}(x)dx
(\partial)/(\partial y)(-2+e^{-x}cos(y))	\frac{\partial\:}{\partial\:y}(-2+e^{-x}\cos(y))
tangent of (2x)/((x^2+1))	tangent\:\frac{2x}{(x^{2}+1)}
limit as x approaches-1 of 2x^2+3x+1	\lim\:_{x\to\:-1}(2x^{2}+3x+1)
integral of 21sqrt(y)	\int\:21\sqrt{y}dy
y^{''}-2/r y^'+2/(r^2)y=0,y(1)=1,y(2)=0	y^{\prime\:\prime\:}-\frac{2}{r}y^{\prime\:}+\frac{2}{r^{2}}y=0,y(1)=1,y(2)=0
integral of 12x^2-48x+36	\int\:12x^{2}-48x+36dx
limit as x approaches 3 of (3x^2-4x-15)/(x^2-5x+6)	\lim\:_{x\to\:3}(\frac{3x^{2}-4x-15}{x^{2}-5x+6})
area x^2+2x+1,3x+3	area\:x^{2}+2x+1,3x+3
derivative of c/(x^2)	\frac{d}{dx}(\frac{c}{x^{2}})
(\partial)/(\partial x)(3y+7)	\frac{\partial\:}{\partial\:x}(3y+7)
integral of ((x^2)/(sqrt(x)))	\int\:(\frac{x^{2}}{\sqrt{x}})dx
integral of e^xsqrt(9+e^x)	\int\:e^{x}\sqrt{9+e^{x}}dx
derivative of 2^{x^2cot(3x})	\frac{d}{dx}(2^{x^{2}\cot(3x)})
derivative of xsin(e^x)	\frac{d}{dx}(x\sin(e^{x}))

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