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Popular Calculus Problems

tangent of 1/(1+x^2)	tangent\:\frac{1}{1+x^{2}}
integral of (27x^2)/(sqrt(x^2-4))	\int\:\frac{27x^{2}}{\sqrt{x^{2}-4}}dx
integral of xsqrt(3x+5)	\int\:x\sqrt{3x+5}dx
integral of sin^4(2x)	\int\:\sin^{4}(2x)dx
(\partial)/(\partial x)(y/((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{y}{(x^{2}+y^{2})})
sum from n=1 to infinity of arctan(5n)	\sum\:_{n=1}^{\infty\:}\arctan(5n)
derivative of In(x^2+9)	\frac{d}{dx}(In(x^{2}+9))
derivative of e^{2x}+e^x	\frac{d}{dx}(e^{2x}+e^{x})
(dy)/(dt)=-3y+12,y(0)=6	\frac{dy}{dt}=-3y+12,y(0)=6
f(x)=(4-x^2)(x+1)	f(x)=(4-x^{2})(x+1)
(dy)/(dx)= 1/10 (500y-y^2)	\frac{dy}{dx}=\frac{1}{10}(500y-y^{2})
(dy)/(dt)=e^{-y}	\frac{dy}{dt}=e^{-y}
integral of 1/9 e^{9x}	\int\:\frac{1}{9}e^{9x}dx
derivative of (6x^2+1/(x^2+9))	\frac{d}{dx}(\frac{6x^{2}+1}{x^{2}+9})
-y^{''}=1	-y^{\prime\:\prime\:}=1
integral of (5x^3-9sqrt(x))/x	\int\:\frac{5x^{3}-9\sqrt{x}}{x}dx
integral of (25)/((x-1)(x^2+4))	\int\:\frac{25}{(x-1)(x^{2}+4)}dx
integral of (x^2+1)^2x	\int\:(x^{2}+1)^{2}xdx
derivative of ln(1-3x)	derivative\:\ln(1-3x)
integral of x^2n^2xx	\int\:x^{2}n^{2}xxdx
integral of x(3-x)	\int\:x(3-x)dx
integral of (5e^x)/(e^{2x)+6e^x+9}	\int\:\frac{5e^{x}}{e^{2x}+6e^{x}+9}dx
integral from 0 to 2 of (4x-x^3)	\int\:_{0}^{2}(4x-x^{3})dx
inverse oflaplace ((4s-3))/((s^2+8s+24))	inverselaplace\:\frac{(4s-3)}{(s^{2}+8s+24)}
area x+2y=7,x+8=y^2	area\:x+2y=7,x+8=y^{2}
integral of 14x^6y^{-4}-12x^5y^{-3}	\int\:14x^{6}y^{-4}-12x^{5}y^{-3}dx
limit as x approaches 3 of sqrt(12-x)-3	\lim\:_{x\to\:3}(\sqrt{12-x}-3)
limit as x approaches infinity of (1+(2/x))^{(x/4)}	\lim\:_{x\to\:\infty\:}((1+(\frac{2}{x}))^{(\frac{x}{4})})
integral from 0 to 3 of x^3-5x	\int\:_{0}^{3}x^{3}-5xdx
(dy)/(dx)= 1/7 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{7}\sqrt{y}\cos^{2}(\sqrt{y})
(ysin(x)+xycos(x))dx+(xsin(x)+1)dy=0	(y\sin(x)+xy\cos(x))dx+(x\sin(x)+1)dy=0
limit as x approaches 0 of x/(e^x)	\lim\:_{x\to\:0}(\frac{x}{e^{x}})
limit as n approaches infinity of ln(n)	\lim\:_{n\to\:\infty\:}(\ln(n))
tangent of x^2+4/x-10,\at x=8	tangent\:x^{2}+\frac{4}{x}-10,\at\:x=8
slope of (-3,5),(-7,-9)	slope\:(-3,5),(-7,-9)
integral of (5x^3)/(sqrt(3+x^2))	\int\:\frac{5x^{3}}{\sqrt{3+x^{2}}}dx
integral of sqrt(x)-1	\int\:\sqrt{x}-1dx
tangent of y=((x-1)/(x+1))	tangent\:y=(\frac{x-1}{x+1})
(\partial)/(\partial x)(x^2y+2x^2-y-2)	\frac{\partial\:}{\partial\:x}(x^{2}y+2x^{2}-y-2)
limit as x approaches 0+of f(x)	\lim\:_{x\to\:0+}(f(x))
integral of (y^2)/(1+x^2)	\int\:\frac{y^{2}}{1+x^{2}}dx
laplacetransform f(t)=7t+3	laplacetransform\:f(t)=7t+3
integral of x/((x+2)(3x-1))	\int\:\frac{x}{(x+2)(3x-1)}dx
integral from 1 to 4 of 1/(sqrt(x-1))	\int\:_{1}^{4}\frac{1}{\sqrt{x-1}}dx
integral of ln(1-x)	\int\:\ln(1-x)dx
(dy)/(dt)=2(t+1)y,y(0)=1	\frac{dy}{dt}=2(t+1)y,y(0)=1
derivative of e^x-xe^x	\frac{d}{dx}(e^{x}-xe^{x})
integral from 1 to 2 of 3r^4ln(r)	\int\:_{1}^{2}3r^{4}\ln(r)dr
integral of (3x)/(4-2x^2)	\int\:\frac{3x}{4-2x^{2}}dx
derivative of-(25000/(x^2)+10)	\frac{d}{dx}(-\frac{25000}{x^{2}}+10)
derivative of (4x^5+5/(x^3))	\frac{d}{dx}(\frac{4x^{5}+5}{x^{3}})
integral from 2 to 7 of 1/(sqrt(x^2-4))	\int\:_{2}^{7}\frac{1}{\sqrt{x^{2}-4}}dx
derivative of (25)/(t^2)-5/t	derivative\:\frac{25}{t^{2}}-\frac{5}{t}
derivative of xe^{2x}(arcsin(3x))	\frac{d}{dx}(xe^{2x}(\arcsin(3x)))
1200(dy)/(dx)=12000-200y-1800	1200\frac{dy}{dx}=12000-200y-1800
integral of (-2)/(x^6)	\int\:\frac{-2}{x^{6}}dx
tangent of f(x)=(7x)/(x+7),(3,2.1)	tangent\:f(x)=\frac{7x}{x+7},(3,2.1)
sum from n=1 to infinity of (1/3)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{3})^{n-1}
integral of xsqrt(144-x^2)	\int\:x\sqrt{144-x^{2}}dx
integral of 3xe-2x	\int\:3xe-2xdx
integral of (y^2-2y+4)/(y(y-2)^2)	\int\:\frac{y^{2}-2y+4}{y(y-2)^{2}}dy
y^{''''}-y^{''}=4x+2xe^{-x}	y^{\prime\:\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}=4x+2xe^{-x}
slope of (1.4)(7.1)	slope\:(1.4)(7.1)
integral from 3 to 9 of 1/(x(ln(x))^2)	\int\:_{3}^{9}\frac{1}{x(\ln(x))^{2}}dx
derivative of f(x)=(1-4x)/(3+x)	derivative\:f(x)=\frac{1-4x}{3+x}
limit as x approaches 5 of ln(x-4)+1/2	\lim\:_{x\to\:5}(\ln(x-4)+\frac{1}{2})
integral of none	\int\:nonedx
integral of (e^{1/(x^3)})/(x^4)	\int\:\frac{e^{\frac{1}{x^{3}}}}{x^{4}}dx
(\partial)/(\partial x)(8x^2cos(5)x^3)	\frac{\partial\:}{\partial\:x}(8x^{2}\cos(5)x^{3})
derivative of (ln(x)/(e^x))	\frac{d}{dx}(\frac{\ln(x)}{e^{x}})
integral from 0 to 2 of 1/(sqrt(9-x^2))	\int\:_{0}^{2}\frac{1}{\sqrt{9-x^{2}}}dx
derivative of f(x)=3x^4	derivative\:f(x)=3x^{4}
limit as x approaches 7 of (x^2-4)/(7-x)	\lim\:_{x\to\:7}(\frac{x^{2}-4}{7-x})
integral of arctan(5t)	\int\:\arctan(5t)dt
limit as x approaches 0 of (x^2+1)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}+1}{x^{2}})
derivative of y= 1/(x(8+ln(x)))	derivative\:y=\frac{1}{x(8+\ln(x))}
integral of e^{-3x}cos(2x)	\int\:e^{-3x}\cos(2x)dx
(5x+2)+(5y-5)y^'=0	(5x+2)+(5y-5)y^{\prime\:}=0
tangent of (4x)/(x^2+1)(1.1)	tangent\:\frac{4x}{x^{2}+1}(1.1)
integral of (\sqrt[3]{x^8})	\int\:(\sqrt[3]{x^{8}})dx
integral of 1/(13x)	\int\:\frac{1}{13x}dx
y^2(1-x^2)^{1/2}dy=arcsin(x)dx	y^{2}(1-x^{2})^{\frac{1}{2}}dy=\arcsin(x)dx
integral of-x^2-2x+3	\int\:-x^{2}-2x+3dx
integral of (2x+1)/(x^2+x+3)	\int\:\frac{2x+1}{x^{2}+x+3}dx
derivative of f(x)=(x^2-81)/(x-9)	derivative\:f(x)=\frac{x^{2}-81}{x-9}
integral of sin(12x)cos(3x)	\int\:\sin(12x)\cos(3x)dx
derivative of (x^2/((1-y^2)))	\frac{d}{dx}(\frac{x^{2}}{(1-y^{2})})
integral of ((y^2)/4)^2	\int\:(\frac{y^{2}}{4})^{2}dy
integral of 1/(10(x+2))	\int\:\frac{1}{10(x+2)}dx
integral of 4cot^3(x)csc^3(x)	\int\:4\cot^{3}(x)\csc^{3}(x)dx
tangent of y=\sqrt[5]{2x^3+8x},(2,2)	tangent\:y=\sqrt[5]{2x^{3}+8x},(2,2)
limit as x approaches 0 of (sin(0))/0	\lim\:_{x\to\:0}(\frac{\sin(0)}{0})
area x^3-3x^2-9x+27,x+3	area\:x^{3}-3x^{2}-9x+27,x+3
limit as x approaches 2 of x^2+2x+3	\lim\:_{x\to\:2}(x^{2}+2x+3)
area y=4x+12,y=x^2	area\:y=4x+12,y=x^{2}
derivative of y=5x^{10}e^x	derivative\:y=5x^{10}e^{x}
integral of xsin(4)x^2	\int\:x\sin(4)x^{2}dx
laplacetransform f(t)=t^2-2t	laplacetransform\:f(t)=t^{2}-2t
integral of (x^2-17x+4)/(x+7)	\int\:\frac{x^{2}-17x+4}{x+7}dx
derivative of x^2+4x-8	\frac{d}{dx}(x^{2}+4x-8)

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