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Popular Calculus Problems

(\partial}{\partial x}(\frac{2-x)/2)	\frac{\partial\:}{\partial\:x}(\frac{2-x}{2})
integral from 2 to 3 of 8/(sqrt(3-x))	\int\:_{2}^{3}\frac{8}{\sqrt{3-x}}dx
derivative of f(s)=sqrt((s^2+1)/(s^2+4))	derivative\:f(s)=\sqrt{\frac{s^{2}+1}{s^{2}+4}}
integral of cos^4(x)	\int\:\cos^{4}(x)dx
(\partial)/(\partial y)(sqrt(xy^2))	\frac{\partial\:}{\partial\:y}(\sqrt{xy^{2}})
limit as x approaches 0+of e^{-x}	\lim\:_{x\to\:0+}(e^{-x})
(\partial)/(\partial x)((x^2+5xy-2y)^8)	\frac{\partial\:}{\partial\:x}((x^{2}+5xy-2y)^{8})
laplacetransform e^{-5t}sin(7t)	laplacetransform\:e^{-5t}\sin(7t)
derivative of arctan(sqrt(2x^3))	\frac{d}{dx}(\arctan(\sqrt{2x^{3}}))
integral of 8\sqrt[4]{x}	\int\:8\sqrt[4]{x}dx
integral of ((5x+7))/(x^2+4x+4)	\int\:\frac{(5x+7)}{x^{2}+4x+4}dx
derivative of 10000-9000e^{-0.3x}	\frac{d}{dx}(10000-9000e^{-0.3x})
derivative of (x^2/(e^{3-4x)})	\frac{d}{dx}(\frac{x^{2}}{e^{3-4x}})
derivative of 9/(sin(x)+cos(x))	derivative\:\frac{9}{\sin(x)+\cos(x)}
derivative of (3x/8)	\frac{d}{dx}(\frac{3x}{8})
integral of ((x^3))/(sqrt(1-x^2))	\int\:\frac{(x^{3})}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial s)(rln(r^2+s^2))	\frac{\partial\:}{\partial\:s}(r\ln(r^{2}+s^{2}))
derivative of (80/x)	\frac{d}{dx}(\frac{80}{x})
y^{''}-3y^'+2y=2e^x(1-x)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=2e^{x}(1-x)
taylor 5xe^x	taylor\:5xe^{x}
limit as x approaches 0 of (3-2x)/(x^4)	\lim\:_{x\to\:0}(\frac{3-2x}{x^{4}})
integral of (3x^2-5x-17)/((x+3)(x-2)^2)	\int\:\frac{3x^{2}-5x-17}{(x+3)(x-2)^{2}}dx
(\partial)/(\partial x)(2x^3y-1)	\frac{\partial\:}{\partial\:x}(2x^{3}y-1)
integral of (e^x+x^2-2^x)	\int\:(e^{x}+x^{2}-2^{x})dx
1/8 (d^2x)/(dt^2)=-2x-1(dx)/(dt)	\frac{1}{8}\frac{d^{2}x}{dt^{2}}=-2x-1\frac{dx}{dt}
integral of (2x-4)(x+2)	\int\:(2x-4)(x+2)dx
area sqrt(x-4),x=8	area\:\sqrt{x-4},x=8
(\partial)/(\partial x)(e^x+z^2)	\frac{\partial\:}{\partial\:x}(e^{x}+z^{2})
2(y-4x^2)dx+xdy=0	2(y-4x^{2})dx+xdy=0
integral of 1/(cos^2(x)+3sin^2(x))	\int\:\frac{1}{\cos^{2}(x)+3\sin^{2}(x)}dx
integral of (x^2+2)/(x+2)	\int\:\frac{x^{2}+2}{x+2}dx
(\partial)/(\partial y)(2x+y)	\frac{\partial\:}{\partial\:y}(2x+y)
integral of (x^{1.5}+11x^{4.5})	\int\:(x^{1.5}+11x^{4.5})dx
derivative of 8xe^xcsc(x)	derivative\:8xe^{x}\csc(x)
integral of 5/(4-2x)	\int\:\frac{5}{4-2x}dx
integral of 1/(sqrt(289-x^2))	\int\:\frac{1}{\sqrt{289-x^{2}}}dx
derivative of sin(4x-1/3 cos^2(4x))	\frac{d}{dx}(\sin(4x)-\frac{1}{3}\cos^{2}(4x))
sum from n=1 to infinity of 3(1/2)^{2n-2}	\sum\:_{n=1}^{\infty\:}3(\frac{1}{2})^{2n-2}
integral from-infinity to pi of e^x	\int\:_{-\infty\:}^{π}e^{x}dx
tangent of (x^2+4)y=8,(2,1)	tangent\:(x^{2}+4)y=8,(2,1)
area 4sqrt(x),4x	area\:4\sqrt{x},4x
integral of-0.5x	\int\:-0.5xdx
limit as x approaches 0 of (e^{6x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{6x}-1}{x})
(\partial}{\partial x}(\frac{(a{R}(x)+b+c{R}(x)+de+{f}(x)+{g}(x)e))/x)	\frac{\partial\:}{\partial\:x}(\frac{(a{R}(x)+b+c{R}(x)+de+{f}(x)+{g}(x)e)}{x})
yln(x)y^'=(((y+1))/(x^{(1/2))})^2	y\ln(x)y^{\prime\:}=(\frac{(y+1)}{x^{(\frac{1}{2})}})^{2}
integral of e^{5x}	\int\:e^{5x}dx
integral of 12x^5	\int\:12x^{5}dx
(\partial)/(\partial t)(-te^tsin(x))	\frac{\partial\:}{\partial\:t}(-te^{t}\sin(x))
integral from 0 to 5 of \|2x-5\|	\int\:_{0}^{5}\left\|2x-5\right\|dx
derivative of sqrt(2x+6)	\frac{d}{dx}(\sqrt{2x+6})
derivative of y=x(x^2+7)^4	derivative\:y=x(x^{2}+7)^{4}
(\partial)/(\partial x)(4e^{xy})	\frac{\partial\:}{\partial\:x}(4e^{xy})
area y=x,y=4,x=0,x=2sqrt(2)	area\:y=x,y=4,x=0,x=2\sqrt{2}
(dy)/(dx)=((x^2+2)/(3y^2))	\frac{dy}{dx}=(\frac{x^{2}+2}{3y^{2}})
(\partial)/(\partial m)(1/2 mv^2)	\frac{\partial\:}{\partial\:m}(\frac{1}{2}mv^{2})
y^{''}+8.2176+207.36y=0,y(0)=0,y^'(0)=-10	y^{\prime\:\prime\:}+8.2176+207.36y=0,y(0)=0,y^{\prime\:}(0)=-10
integral of e^{1-x^2}	\int\:e^{1-x^{2}}dx
integral of (3e^x-1/3 x^3)	\int\:(3e^{x}-\frac{1}{3}x^{3})dx
integral of 13xe^{-x^2}	\int\:13xe^{-x^{2}}dx
(\partial)/(\partial x)(2x^3y+sin(x^4))	\frac{\partial\:}{\partial\:x}(2x^{3}y+\sin(x^{4}))
integral of (-4x)/(e^{x^2)}	\int\:\frac{-4x}{e^{x^{2}}}dx
d/(dy)(3xe^{-1/(y^3)}-20x^3)	\frac{d}{dy}(3xe^{-\frac{1}{y^{3}}}-20x^{3})
tangent of f(x)=x-1/x+ln(x),\at x=1	tangent\:f(x)=x-\frac{1}{x}+\ln(x),\at\:x=1
tangent of y=16xsin(x),(pi/2 ,8pi)	tangent\:y=16x\sin(x),(\frac{π}{2},8π)
(\partial)/(\partial y)(xln(y+z))	\frac{\partial\:}{\partial\:y}(x\ln(y+z))
integral of 3/(x-3)	\int\:\frac{3}{x-3}dx
derivative of x^2-10	derivative\:x^{2}-10
derivative of ln(x^4+2)	derivative\:\ln(x^{4}+2)
(dy)/(dx)=2y-x	\frac{dy}{dx}=2y-x
sum from n=7 to infinity of e^{7-2n}	\sum\:_{n=7}^{\infty\:}e^{7-2n}
derivative of (15/x+(225)/(15-x))	\frac{d}{dx}(\frac{15}{x}+\frac{225}{15-x})
xyy^'=x^6+3y^2,y(e)=-e^3	xyy^{\prime\:}=x^{6}+3y^{2},y(e)=-e^{3}
derivative of (3x^3+4(x^4-2x))	\frac{d}{dx}((3x^{3}+4)(x^{4}-2x))
limit as x approaches 0 of (x^2ln(x))/x	\lim\:_{x\to\:0}(\frac{x^{2}\ln(x)}{x})
(\partial)/(\partial x)((y-2)(arctan(x)))	\frac{\partial\:}{\partial\:x}((y-2)(\arctan(x)))
derivative of (csc(x)/(2^x))	\frac{d}{dx}(\frac{\csc(x)}{2^{x}})
limit as x approaches 0 of (x^2-2x)/x	\lim\:_{x\to\:0}(\frac{x^{2}-2x}{x})
derivative of-sin(5x)	\frac{d}{dx}(-\sin(5x))
integral of (sqrt(4+x^2))/(x^2)	\int\:\frac{\sqrt{4+x^{2}}}{x^{2}}dx
integral from 0 to 2pi of sin^2(8x)	\int\:_{0}^{2π}\sin^{2}(8x)dx
derivative of 10xln(100x)	\frac{d}{dx}(10x\ln(100x))
(\partial)/(\partial y)(27xy^2+8y^3)	\frac{\partial\:}{\partial\:y}(27xy^{2}+8y^{3})
limit as x approaches 2 of 4x-5	\lim\:_{x\to\:2}(4x-5)
integral of (1-x+2x^2-x^3)/(x^5+2x^3+x)	\int\:\frac{1-x+2x^{2}-x^{3}}{x^{5}+2x^{3}+x}dx
integral from 0 to 1 of 6(1+sqrt(x))^8	\int\:_{0}^{1}6(1+\sqrt{x})^{8}dx
integral from 2 to 3 of (10)/(x^2-1)	\int\:_{2}^{3}\frac{10}{x^{2}-1}dx
y^'=10y^2sin(x)	y^{\prime\:}=10y^{2}\sin(x)
integral from 0 to 8 of pi(x+1)^2	\int\:_{0}^{8}π(x+1)^{2}dx
integral of sin^{1/2}(2z)cos^3(2z)	\int\:\sin^{\frac{1}{2}}(2z)\cos^{3}(2z)dz
(sqrt(2))^'	(\sqrt{2})^{\prime\:}
integral of (8x^3+1/x)	\int\:(8x^{3}+\frac{1}{x})dx
limit as x approaches-infinity of 8e^{x+9}	\lim\:_{x\to\:-\infty\:}(8e^{x+9})
derivative of f(x)=3e^{3e^x+x}	derivative\:f(x)=3e^{3e^{x}+x}
(\partial)/(\partial x)(xz+e^{-x^2+y})	\frac{\partial\:}{\partial\:x}(xz+e^{-x^{2}+y})
derivative of 4^x+1	\frac{d}{dx}(4^{x}+1)
derivative of x^2+3x+5	\frac{d}{dx}(x^{2}+3x+5)
limit as x approaches 2 of 4/((x-2)^3)	\lim\:_{x\to\:2}(\frac{4}{(x-2)^{3}})
derivative of dcos(x+x^2sin(x))	\frac{d}{dx}(d\cos(x)+x^{2}\sin(x))
sum from n=1 to infinity of 3/(n^{5/3)}	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{\frac{5}{3}}}
slope of \|x\|+3	slope\:\left\|x\right\|+3

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