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Popular Calculus Problems

y^'=x^2sec(y)	y^{\prime\:}=x^{2}\sec(y)
integral from 0 to 1 of xe^{-3x^2}	\int\:_{0}^{1}xe^{-3x^{2}}dx
sum from n=0 to infinity of arctan(2n)	\sum\:_{n=0}^{\infty\:}\arctan(2n)
slope of (2,2),(0,-1)	slope\:(2,2),(0,-1)
limit as x approaches 0-of 5/(sin(x))	\lim\:_{x\to\:0-}(\frac{5}{\sin(x)})
laplacetransform acos(2pi+θ)	laplacetransform\:a\cos(2π+θ)
(dy)/(dt)=-4y+3e^{-t}	\frac{dy}{dt}=-4y+3e^{-t}
integral of \sqrt[3]{x^2}+xsqrt(x)	\int\:\sqrt[3]{x^{2}}+x\sqrt{x}dx
limit as x approaches 0 of (x^2-9x)/x	\lim\:_{x\to\:0}(\frac{x^{2}-9x}{x})
slope of (3,3),(2,-2)	slope\:(3,3),(2,-2)
integral of xcos(n)x	\int\:x\cos(n)xdx
derivative of (x+3ln(x^2))	\frac{d}{dx}((x+3)\ln(x^{2}))
y+2y^7=(y^3+6x)y^'	y+2y^{7}=(y^{3}+6x)y^{\prime\:}
derivative of x^2-x	derivative\:x^{2}-x
limit as x approaches 0+of x/(x+1)	\lim\:_{x\to\:0+}(\frac{x}{x+1})
(\partial)/(\partial x)((x+2y+3z)^{3/2})	\frac{\partial\:}{\partial\:x}((x+2y+3z)^{\frac{3}{2}})
derivative of y=6e^{3x}	derivative\:y=6e^{3x}
derivative of 6x^2+5	\frac{d}{dx}(6x^{2}+5)
integral of 1/(x^2*sqrt(x^2+1))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{x^{2}+1}}dx
integral of 8/(9+r^2)	\int\:\frac{8}{9+r^{2}}dr
derivative of f(x)=((4x)^3)/((3-5x)^5)	derivative\:f(x)=\frac{(4x)^{3}}{(3-5x)^{5}}
integral of 4xln(4x)	\int\:4x\ln(4x)dx
derivative of ln(e^xsqrt(x))	derivative\:\ln(e^{x}\sqrt{x})
taylor 1/(1-x),(pi/4)	taylor\:\frac{1}{1-x},(\frac{π}{4})
integral of ((2x+1))/((x+2)^4(x-1)^4)	\int\:\frac{(2x+1)}{(x+2)^{4}(x-1)^{4}}dx
(dy)/(dx)=3x^2e^{-y}	\frac{dy}{dx}=3x^{2}e^{-y}
inverse oflaplace 1/(2s+2)	inverselaplace\:\frac{1}{2s+2}
integral of (x^4)/(1+x^{10)}	\int\:\frac{x^{4}}{1+x^{10}}dx
integral of 3e^{2x+e^{2x}}	\int\:3e^{2x+e^{2x}}dx
tangent of 6/x	tangent\:\frac{6}{x}
integral of (2x^4-1)(5x^3+6x)	\int\:(2x^{4}-1)(5x^{3}+6x)dx
slope of f(-3)=-2x^2+4x-7/(x^2)	slope\:f(-3)=-2x^{2}+4x-\frac{7}{x^{2}}
(dy)/(dx)=y(xy^4-1)	\frac{dy}{dx}=y(xy^{4}-1)
f(x)=-4/x	f(x)=-\frac{4}{x}
sum from n=0 to infinity of 5(3/4)^n	\sum\:_{n=0}^{\infty\:}5(\frac{3}{4})^{n}
integral of sech^4(x)tanh(x)	\int\:\sech^{4}(x)\tanh(x)dx
4xy^'+4y=3	4xy^{\prime\:}+4y=3
area x^5+1,x+1,-1,0	area\:x^{5}+1,x+1,-1,0
5x-6ysqrt(x^2+1)(dy)/(dx)=0	5x-6y\sqrt{x^{2}+1}\frac{dy}{dx}=0
limit as x approaches 2 of x^2-3x+8	\lim\:_{x\to\:2}(x^{2}-3x+8)
integral of-2x^6sin(3x)	\int\:-2x^{6}\sin(3x)dx
inverse oflaplace ((s+5))/(s^2+5s+4)	inverselaplace\:\frac{(s+5)}{s^{2}+5s+4}
derivative of xsqrt(2x+5)	\frac{d}{dx}(x\sqrt{2x+5})
integral of (x^2+x^{-2})/(x^3-3x^{-1)}	\int\:\frac{x^{2}+x^{-2}}{x^{3}-3x^{-1}}dx
y^'+7(tan(7x))y=5cos(7x)	y^{\prime\:}+7(\tan(7x))y=5\cos(7x)
derivative of (x^5)/(x^3)	derivative\:\frac{x^{5}}{x^{3}}
integral of 5/(x^2sqrt(x^2-9))	\int\:\frac{5}{x^{2}\sqrt{x^{2}-9}}dx
derivative of xe^{-x^2y}	\frac{d}{dx}(xe^{-x^{2}y})
(d^2)/(dx^2)(3xsin(x^2))	\frac{d^{2}}{dx^{2}}(3x\sin(x^{2}))
integral of x/(x-9)	\int\:\frac{x}{x-9}dx
integral of 1/(xsqrt(x^3-1))	\int\:\frac{1}{x\sqrt{x^{3}-1}}dx
integral of (-3)/(x^2)+11-4^x	\int\:\frac{-3}{x^{2}}+11-4^{x}dx
derivative of sin^5(x^3)	derivative\:\sin^{5}(x^{3})
limit as x approaches 5 of \|x-5\|	\lim\:_{x\to\:5}(\left\|x-5\right\|)
y^'-y/2 =e^{-t}	y^{\prime\:}-\frac{y}{2}=e^{-t}
(e^x-y)dx+(e^y-x)dy=0	(e^{x}-y)dx+(e^{y}-x)dy=0
(x+1)(dy)/(dx)=x+6	(x+1)\frac{dy}{dx}=x+6
integral of-2/(sqrt(100-9t^2))	\int\:-\frac{2}{\sqrt{100-9t^{2}}}dt
limit as x approaches-1 of sin((pix)/6)	\lim\:_{x\to\:-1}(\sin(\frac{πx}{6}))
integral of 4x^{3/2}	\int\:4x^{\frac{3}{2}}dx
(\partial)/(\partial x)(sqrt(x^2+y^2-5))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}-5})
integral from 0 to pi/2 of cos((2x)/3)	\int\:_{0}^{\frac{π}{2}}\cos(\frac{2x}{3})dx
tangent of f(x)=x^3-x,\at x=1	tangent\:f(x)=x^{3}-x,\at\:x=1
derivative of xsqrt(3x-4)	derivative\:x\sqrt{3x-4}
sum from n=1 to infinity of 2(-e)^{-n}	\sum\:_{n=1}^{\infty\:}2(-e)^{-n}
integral of (x^5)/(sqrt(x^2+7))	\int\:\frac{x^{5}}{\sqrt{x^{2}+7}}dx
integral of 1/(sqrt(5+4x-x^2))	\int\:\frac{1}{\sqrt{5+4x-x^{2}}}dx
limit as x approaches-infinity of ((sqrt(4x^2+1)))/((2-7x))	\lim\:_{x\to\:-\infty\:}(\frac{(\sqrt{4x^{2}+1})}{(2-7x)})
xy^'+4y=-25xsin(x^5)	xy^{\prime\:}+4y=-25x\sin(x^{5})
derivative of 3/(sqrt(7x^4-5x^2+1))	\frac{d}{dx}(\frac{3}{\sqrt{7x^{4}-5x^{2}+1}})
(dy)/(dx)=tan(4x)	\frac{dy}{dx}=\tan(4x)
integral of sqrt(16-t^2)	\int\:\sqrt{16-t^{2}}dt
(\partial)/(\partial y)(1-x-y)	\frac{\partial\:}{\partial\:y}(1-x-y)
limit as x approaches 0.1 of (e^x-1)/x	\lim\:_{x\to\:0.1}(\frac{e^{x}-1}{x})
integral from 2 to 3 of (29)/(sqrt(3-x))	\int\:_{2}^{3}\frac{29}{\sqrt{3-x}}dx
derivative of f(x)=(6x-x^2)^{10}	derivative\:f(x)=(6x-x^{2})^{10}
derivative of sin^5(3x)	\frac{d}{dx}(\sin^{5}(3x))
derivative of 5ln(x)+cos(x)	derivative\:5\ln(x)+\cos(x)
y^'=(y+8)/(x+6)	y^{\prime\:}=\frac{y+8}{x+6}
integral of e^x+y	\int\:e^{x}+ydx
integral of cos(r^2)r	\int\:\cos(r^{2})rdr
limit as x approaches 3 of (x-3)/(x+6)	\lim\:_{x\to\:3}(\frac{x-3}{x+6})
derivative of y=10^{3x}	derivative\:y=10^{3x}
y^'=4-9x^2-6x^5	y^{\prime\:}=4-9x^{2}-6x^{5}
integral from 0 to 2 of 8x-4x^2	\int\:_{0}^{2}8x-4x^{2}dx
derivative of cos(x+sin(x)+1/2 x^2+1/x)	\frac{d}{dx}(\cos(x)+\sin(x)+\frac{1}{2}x^{2}+\frac{1}{x})
integral of sin(20x)cos(15x)	\int\:\sin(20x)\cos(15x)dx
integral of (3^x+2/x)	\int\:(3^{x}+\frac{2}{x})dx
integral from 2 to 5 of 1/(sqrt(x-1))	\int\:_{2}^{5}\frac{1}{\sqrt{x-1}}dx
integral of x^2(2x^3+4)^5	\int\:x^{2}(2x^{3}+4)^{5}dx
integral of x/k	\int\:\frac{x}{k}dx
taylor x^2+x^31	taylor\:x^{2}+x^{3}1
derivative of (4t^2-t)(t^3-8t^2+12)	derivative\:(4t^{2}-t)(t^{3}-8t^{2}+12)
area y=sin(x),y=2sin^2(x),x=0,x= pi/2	area\:y=\sin(x),y=2\sin^{2}(x),x=0,x=\frac{π}{2}
limit as x approaches pi-of x/(cos(x)+1)	\lim\:_{x\to\:π-}(\frac{x}{\cos(x)+1})
y^{''}+4y^'+3y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=0
limit as x approaches 0-of 4+6/(x^2)	\lim\:_{x\to\:0-}(4+\frac{6}{x^{2}})
tangent of f(x)=x^2,\at x=-1	tangent\:f(x)=x^{2},\at\:x=-1
integral of 1/(sqrt(z))	\int\:\frac{1}{\sqrt{z}}dz
(dx)/(dt)+5tx^3+x/t =0	\frac{dx}{dt}+5tx^{3}+\frac{x}{t}=0

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