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Popular Calculus Problems

sum from n=2 to infinity of (n+2)/(2n+3)	\sum\:_{n=2}^{\infty\:}\frac{n+2}{2n+3}
limit as x approaches 1 of x(2)	\lim\:_{x\to\:1}(x(2))
derivative of ax^2+by(x^2+λ(x^2+y^2-c^2))	\frac{d}{dx}(ax^{2}+by(x)^{2}+λ(x^{2}+y^{2}-c^{2}))
x^2-2xy+xy^'=0	x^{2}-2xy+xy^{\prime\:}=0
integral of (x+4)/(x^2+5x+4)	\int\:\frac{x+4}{x^{2}+5x+4}dx
limit as x approaches 3+of ln(x^2-9)	\lim\:_{x\to\:3+}(\ln(x^{2}-9))
(-1/((1+x)^2))^'	(-\frac{1}{(1+x)^{2}})^{\prime\:}
integral of (a+bx^2)/(sqrt(3ax+bx^3))	\int\:\frac{a+bx^{2}}{\sqrt{3ax+bx^{3}}}dx
derivative of arccos(3x)	\frac{d}{dx}(\arccos(3x))
t(dy)/(dt)+21y= 1/t	t\frac{dy}{dt}+21y=\frac{1}{t}
integral from 0 to x of (t^3-t)^5	\int\:_{0}^{x}(t^{3}-t)^{5}dt
derivative of 10+(50x)/(2x^2+9)	derivative\:10+\frac{50x}{2x^{2}+9}
integral of e^xsin(5x)	\int\:e^{x}\sin(5x)dx
integral of sqrt(5-3x^2)	\int\:\sqrt{5-3x^{2}}dx
(\partial)/(\partial x)(4xsin(9x^2y))	\frac{\partial\:}{\partial\:x}(4x\sin(9x^{2}y))
derivative of arccos(x/3)	\frac{d}{dx}(\arccos(\frac{x}{3}))
derivative of sqrt(3x^2-1)	\frac{d}{dx}(\sqrt{3x^{2}-1})
integral from 0 to 2 of (6-4ln(3-x))^2	\int\:_{0}^{2}(6-4\ln(3-x))^{2}dx
integral of 9sqrt(x)	\int\:9\sqrt{x}dx
yy^'=t	yy^{\prime\:}=t
derivative of f(x)=\|x-4\|	derivative\:f(x)=\left\|x-4\right\|
derivative of 1/((3x^3+5x+4^{3/4)})	\frac{d}{dx}(\frac{1}{(3x^{3}+5x+4)^{\frac{3}{4}}})
derivative of (f(x(6x))^2+3)	\frac{d}{dx}((f(x)(6x))^{2}+3)
(\partial)/(\partial y)(2e^{xy})	\frac{\partial\:}{\partial\:y}(2e^{xy})
(\partial)/(\partial x)(x^2y+3xy^4)	\frac{\partial\:}{\partial\:x}(x^{2}y+3xy^{4})
limit as x approaches 0 of x/(e^{-3x)-1}	\lim\:_{x\to\:0}(\frac{x}{e^{-3x}-1})
3x^'+6x=4,x(0)=2	3x^{\prime\:}+6x=4,x(0)=2
derivative of 1100sqrt(x^2-0.2x)	\frac{d}{dx}(1100\sqrt{x^{2}-0.2x})
taylor sin(2x)	taylor\:\sin(2x)
derivative of 16x	\frac{d}{dx}(16x)
derivative of (5a+1)^2	derivative\:(5a+1)^{2}
integral from 0.2 to 0.4 of (200x)	\int\:_{0.2}^{0.4}(200x)dx
integral of x^{1/3}-x	\int\:x^{\frac{1}{3}}-xdx
derivative of sex	\frac{d}{dx}(sex)
derivative of sqrt(x)-5	\frac{d}{dx}(\sqrt{x}-5)
integral of e^6	\int\:e^{6}
integral of (3x-5)^5	\int\:(3x-5)^{5}dx
integral of (8ln(x))/x	\int\:\frac{8\ln(x)}{x}dx
derivative of-1/(x^2e^{1/x})	\frac{d}{dx}(-\frac{1}{x^{2}}e^{\frac{1}{x}})
derivative of x^4y^5+2xmy(x^2-4y^3a)	\frac{d}{dx}(x^{4}y^{5}+2xmy(x)^{2}-4y^{3}a)
integral of ((2x+4))/((x^2+5x-6))	\int\:\frac{(2x+4)}{(x^{2}+5x-6)}dx
derivative of (x+y(x-y))	\frac{d}{dx}((x+y)(x-y))
integral of (2x^2-3x+2)/(x^3-3x^2+2x)	\int\:\frac{2x^{2}-3x+2}{x^{3}-3x^{2}+2x}dx
integral of 1/(2x^2+8x+20)	\int\:\frac{1}{2x^{2}+8x+20}dx
integral of 8^x	\int\:8^{x}dx
integral of 4tan^4(x)sec^6(x)	\int\:4\tan^{4}(x)\sec^{6}(x)dx
integral of (x^2-x+1)/(x^2(x^2+1))	\int\:\frac{x^{2}-x+1}{x^{2}(x^{2}+1)}dx
integral of x/(\sqrt[4]{x+9)}	\int\:\frac{x}{\sqrt[4]{x+9}}dx
derivative of x^3+2x^2-x-1	\frac{d}{dx}(x^{3}+2x^{2}-x-1)
integral from 1 to 2 of (x^2+1)/(x^2)	\int\:_{1}^{2}\frac{x^{2}+1}{x^{2}}dx
derivative of x\sqrt[3]{x}	derivative\:x\sqrt[3]{x}
laplacetransform sin(t+1)	laplacetransform\:\sin(t+1)
integral from 0 to 4 of x^2-4x	\int\:_{0}^{4}x^{2}-4xdx
derivative of 1/(t+1)	derivative\:\frac{1}{t+1}
integral of te^{-5t}	\int\:te^{-5t}dt
limit as x approaches 5 of x^2-8x+15	\lim\:_{x\to\:5}(x^{2}-8x+15)
limit as x approaches 0 of 2/(sqrt(x))	\lim\:_{x\to\:0}(\frac{2}{\sqrt{x}})
derivative of f(x)=x^2(2/(x^2)+5/(x^3))	derivative\:f(x)=x^{2}(\frac{2}{x^{2}}+\frac{5}{x^{3}})
integral of (sqrt(x^2-64))/(x^4)	\int\:\frac{\sqrt{x^{2}-64}}{x^{4}}dx
integral from 0 to 4 of 5/(6x^2+7x+1)	\int\:_{0}^{4}\frac{5}{6x^{2}+7x+1}dx
(dy)/(dx)+8y=11	\frac{dy}{dx}+8y=11
area x=0,x=1,y=6+x^4	area\:x=0,x=1,y=6+x^{4}
integral of x^3sinh(x)	\int\:x^{3}\sinh(x)dx
limit as x approaches 6+of 7-x	\lim\:_{x\to\:6+}(7-x)
integral of ((x+4))/(sqrt(x))	\int\:\frac{(x+4)}{\sqrt{x}}dx
sum from n=1 to infinity of n+1	\sum\:_{n=1}^{\infty\:}n+1
derivative of y=2\sqrt[5]{x^2}+4	derivative\:y=2\sqrt[5]{x^{2}}+4
integral of 3/65 x^2	\int\:\frac{3}{65}x^{2}dx
integral from 0 to 4 of 4x-x^2	\int\:_{0}^{4}4x-x^{2}dx
integral of xcos((nxpi)/l)	\int\:x\cos(\frac{nxπ}{l})dx
volumeabout y=0,x= 1/3 (y^2+2)^{3/2},[1,3]	volumeabout\:y=0,x=\frac{1}{3}(y^{2}+2)^{\frac{3}{2}},[1,3]
(dy)/(dx)=(3x)/(10y)	\frac{dy}{dx}=\frac{3x}{10y}
integral from 0 to 11 of 1/(121+x^2)	\int\:_{0}^{11}\frac{1}{121+x^{2}}dx
integral of e^{2x}x^2	\int\:e^{2x}x^{2}dx
integral of (2x)/((4+3x^2)^2)	\int\:\frac{2x}{(4+3x^{2})^{2}}dx
tangent of 3cos(3θ)	tangent\:3\cos(3θ)
integral from 0 to 5 of v(t)	\int\:_{0}^{5}v(t)dt
(\partial)/(\partial x)((xy+2)e^{-xy})	\frac{\partial\:}{\partial\:x}((xy+2)e^{-xy})
derivative of-4sin(xcos(x))	\frac{d}{dx}(-4\sin(x)\cos(x))
integral of 3/(sqrt(x+4))	\int\:\frac{3}{\sqrt{x+4}}dx
tangent of f(x)=x^3+x,\at x=2	tangent\:f(x)=x^{3}+x,\at\:x=2
derivative of cos(sin^2(x-2))	derivative\:\cos(\sin^{2}(x-2))
limit as x approaches 0+of arctan(ln(0))	\lim\:_{x\to\:0+}(\arctan(\ln(0)))
(\partial)/(\partial x)(4x^2y^3+1)	\frac{\partial\:}{\partial\:x}(4x^{2}y^{3}+1)
derivative of (3x+2/(2x+3))	\frac{d}{dx}(\frac{3x+2}{2x+3})
integral of e^{2x}sin(x)	\int\:e^{2x}\sin(x)dx
integral of (16x^2-48x+15)/(2x^3-7x^2+3x)	\int\:\frac{16x^{2}-48x+15}{2x^{3}-7x^{2}+3x}dx
derivative of e^0	derivative\:e^{0}
integral of zsqrt(1-z)	\int\:z\sqrt{1-z}dz
limit as x approaches 0 of (x-2)/(\|x-2\|)	\lim\:_{x\to\:0}(\frac{x-2}{\left\|x-2\right\|})
integral from 0 to 4 of sqrt(y)-y+2	\int\:_{0}^{4}\sqrt{y}-y+2dy
derivative of 4x(x^2-4)	\frac{d}{dx}(4x(x^{2}-4))
integral of 1/(2x^2-x)	\int\:\frac{1}{2x^{2}-x}dx
derivative of f(x)=5x-7	derivative\:f(x)=5x-7
derivative of x^3sqrt(2x-1)	\frac{d}{dx}(x^{3}\sqrt{2x-1})
derivative of x^3-x^2-2x	\frac{d}{dx}(x^{3}-x^{2}-2x)
tangent of y=-9x^2,\at x=8	tangent\:y=-9x^{2},\at\:x=8
y^{''}=x^2+1	y^{\prime\:\prime\:}=x^{2}+1
derivative of y=sqrt(1+(2x+1)^8)	derivative\:y=\sqrt{1+(2x+1)^{8}}
integral of (x^2+1)nx	\int\:(x^{2}+1)nxdx

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