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Popular Calculus Problems

integral of (x+4)/(x^2+4)	\int\:\frac{x+4}{x^{2}+4}dx
area (x+2)^3,2x^2-8x+8,0	area\:(x+2)^{3},2x^{2}-8x+8,0
limit as x approaches 1 of x+4-12	\lim\:_{x\to\:1}(x+4-12)
tangent of f(x)=sqrt(x+2),\at x=1	tangent\:f(x)=\sqrt{x+2},\at\:x=1
derivative of f(x)=log_{4}(3x^2+1)	derivative\:f(x)=\log_{4}(3x^{2}+1)
limit as x approaches 14-of 15x+ln(14-x)	\lim\:_{x\to\:14-}(15x+\ln(14-x))
laplacetransform (1+e^{-t})^2	laplacetransform\:(1+e^{-t})^{2}
tangent of y=x^{sin(x)}	tangent\:y=x^{\sin(x)}
derivative of t^2-8t+16	derivative\:t^{2}-8t+16
derivative of (2x^{6x})	\frac{d}{dx}((2x)^{6x})
limit as x approaches-infinity of x^2e^{-3x}	\lim\:_{x\to\:-\infty\:}(x^{2}e^{-3x})
derivative of x-e^x	derivative\:x-e^{x}
integral of (x-1)^{-2}	\int\:(x-1)^{-2}dx
(\partial)/(\partial x)(arccos(x/y))	\frac{\partial\:}{\partial\:x}(\arccos(\frac{x}{y}))
integral of sin^3(11x)cos^2(11x)	\int\:\sin^{3}(11x)\cos^{2}(11x)dx
derivative of (1+1/x ^x)	\frac{d}{dx}((1+\frac{1}{x})^{x})
laplacetransform 0.025sin((2pit)/(10))	laplacetransform\:0.025\sin(\frac{2πt}{10})
derivative of x/((x-2^2))	\frac{d}{dx}(\frac{x}{(x-2)^{2}})
integral from 1 to ln(8) of integral from 0 to ln(y) of e^{x+y}	\int\:_{1}^{\ln(8)}\int\:_{0}^{\ln(y)}e^{x+y}dxdy
(dy)/(dx)= 1/(4x)	\frac{dy}{dx}=\frac{1}{4x}
integral of x/((x^2+1)^{1/2)}	\int\:\frac{x}{(x^{2}+1)^{\frac{1}{2}}}dx
area x^4-9x^2,x^2-9,0,3	area\:x^{4}-9x^{2},x^{2}-9,0,3
integral of x/(x^2+64)	\int\:\frac{x}{x^{2}+64}dx
(dy)/(dx)=7y^2sin(x)	\frac{dy}{dx}=7y^{2}\sin(x)
integral of (e^x)/(2+e^x)	\int\:\frac{e^{x}}{2+e^{x}}dx
(\partial)/(\partial x)(xe^{2xy})	\frac{\partial\:}{\partial\:x}(xe^{2xy})
xy^2(dy)/(dx)=y^3-x^3,y(1)=1	xy^{2}\frac{dy}{dx}=y^{3}-x^{3},y(1)=1
derivative of f(x)-2x^2	derivative\:f(x)-2x^{2}
(\partial)/(\partial x)(x^2y-xy^2)	\frac{\partial\:}{\partial\:x}(x^{2}y-xy^{2})
tangent of f(x)=sqrt(2x+3),(3,3)	tangent\:f(x)=\sqrt{2x+3},(3,3)
derivative of y=6ln(x)-x^3+2\sqrt[3]{x}	derivative\:y=6\ln(x)-x^{3}+2\sqrt[3]{x}
limit as x approaches infinity of arctan(8x)	\lim\:_{x\to\:\infty\:}(\arctan(8x))
integral from 1 to infinity of 9/(x^4)	\int\:_{1}^{\infty\:}\frac{9}{x^{4}}dx
(\partial)/(\partial x)((x^4-1)(x^2+1))	\frac{\partial\:}{\partial\:x}((x^{4}-1)(x^{2}+1))
(\partial)/(\partial y)(ysin(x))	\frac{\partial\:}{\partial\:y}(y\sin(x))
limit as x approaches 2+of sqrt(2^x-4)	\lim\:_{x\to\:2+}(\sqrt{2^{x}-4})
limit as x approaches 1+of ln^x(x)	\lim\:_{x\to\:1+}(\ln^{x}(x))
integral of (4*x+3)/(x^2-25)	\int\:\frac{4\cdot\:x+3}{x^{2}-25}dx
y(x+3)+(dy)/(dx)=0	y(x+3)+\frac{dy}{dx}=0
integral of-7sin(x)+4cos(x)	\int\:-7\sin(x)+4\cos(x)dx
derivative of ln(x/(x-1))	derivative\:\ln(\frac{x}{x-1})
integral of tan^3(2x)sec^5(2x)	\int\:\tan^{3}(2x)\sec^{5}(2x)dx
derivative of e^{2x}cos(4x)	\frac{d}{dx}(e^{2x}\cos(4x))
integral of 4x(2x^2+1)^7	\int\:4x(2x^{2}+1)^{7}dx
integral of 6x^4-5x^3+5x^2+C	\int\:6x^{4}-5x^{3}+5x^{2}+Cdx
(dy)/(dx)=e^{2y-x}	\frac{dy}{dx}=e^{2y-x}
tangent of y=(7x-4)(2+6x)	tangent\:y=(7x-4)(2+6x)
limit as x approaches infinity of arctan(1-x)	\lim\:_{x\to\:\infty\:}(\arctan(1-x))
limit as x approaches 0+of arctan(ln(x))	\lim\:_{x\to\:0+}(\arctan(\ln(x)))
(dv)/(dx)-1/x v=8	\frac{dv}{dx}-\frac{1}{x}v=8
derivative of (ln(x))/(e^x)	derivative\:\frac{\ln(x)}{e^{x}}
limit as x approaches 0 of 5/x-5/(\|x\|)	\lim\:_{x\to\:0}(\frac{5}{x}-\frac{5}{\left\|x\right\|})
area f(x)=x,g(x)=sqrt(x),[0,2]	area\:f(x)=x,g(x)=\sqrt{x},[0,2]
integral from 2 to 25 of sin(2x)	\int\:_{2}^{25}\sin(2x)dx
(\partial)/(\partial x)(dx)	\frac{\partial\:}{\partial\:x}(dx)
integral of (6x+8)	\int\:(6x+8)dx
integral of 1/(sqrt((1-x^2)))	\int\:\frac{1}{\sqrt{(1-x^{2})}}dx
10y^{''}+80y^'+200y=0	10y^{\prime\:\prime\:}+80y^{\prime\:}+200y=0
derivative of f(x)= x/(sqrt(x^2+2))	derivative\:f(x)=\frac{x}{\sqrt{x^{2}+2}}
d/(d{r)}(6((6{r}-1)*k+{r})-1)	\frac{d}{d{r}}(6((6{r}-1)\cdot\:k+{r})-1)
(\partial)/(\partial x)(ln(x/(x+y)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{x+y}))
sum from n=1 to infinity of 1/((n+2)^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{(n+2)^{2}}
tangent of y= 3/(sqrt(16-x)),\at x=0	tangent\:y=\frac{3}{\sqrt{16-x}},\at\:x=0
integral of xe^{-x(y+1)}	\int\:xe^{-x(y+1)}dx
integral of ((2x-1)^2)/(2x)	\int\:\frac{(2x-1)^{2}}{2x}dx
integral from 0 to 1/2 of 1	\int\:_{0}^{\frac{1}{2}}1dx
integral of (3x^2+1)^3	\int\:(3x^{2}+1)^{3}dx
(dy)/(dx)+ycos(x)=2cos(x),y(0)=4	\frac{dy}{dx}+y\cos(x)=2\cos(x),y(0)=4
f(x)=sin(x)ln(2x)	f(x)=\sin(x)\ln(2x)
derivative of sec(θ)	derivative\:\sec(θ)
(\partial)/(\partial y)(2x^3y^2)	\frac{\partial\:}{\partial\:y}(2x^{3}y^{2})
integral of 4xln(2x)	\int\:4x\ln(2x)dx
tangent of f(x)=x^2-5x+5,\at x=a	tangent\:f(x)=x^{2}-5x+5,\at\:x=a
integral of (-x)/(x-1)	\int\:\frac{-x}{x-1}dx
integral of sin^3(θ)cos^4(θ)	\int\:\sin^{3}(θ)\cos^{4}(θ)dθ
integral of 4/(xln^3(x))	\int\:\frac{4}{x\ln^{3}(x)}dx
laplacetransform e^{-(t-3)}	laplacetransform\:e^{-(t-3)}
limit as x approaches 0+of 4/(5x^{1/3)}	\lim\:_{x\to\:0+}(\frac{4}{5x^{\frac{1}{3}}})
(dy}{dx}=\frac{y+sqrt(x^2+y^2))/x	\frac{dy}{dx}=\frac{y+\sqrt{x^{2}+y^{2}}}{x}
derivative of (2x^3-5(x^2-5ln(x)))	\frac{d}{dx}((2x^{3}-5)(x^{2}-5\ln(x)))
derivative of x/(csc(x))	\frac{d}{dx}(\frac{x}{\csc(x)})
f^'(x)=(e^x)/x	f^{\prime\:}(x)=\frac{e^{x}}{x}
(\partial)/(\partial y)(3ze^{xy})	\frac{\partial\:}{\partial\:y}(3ze^{xy})
integral of (2x+32)/(x^2+8x+7)	\int\:\frac{2x+32}{x^{2}+8x+7}dx
derivative of y= 1/2 x^3	derivative\:y=\frac{1}{2}x^{3}
derivative of 1/((x+7^2))	\frac{d}{dx}(\frac{1}{(x+7)^{2}})
parity f(x)=x*tan(x^2)	parity\:f(x)=x\cdot\:\tan(x^{2})
(\partial)/(\partial y)(3x^2y+e^y)	\frac{\partial\:}{\partial\:y}(3x^{2}y+e^{y})
derivative of y=8sqrt(x)+6x^{3/4}	derivative\:y=8\sqrt{x}+6x^{\frac{3}{4}}
(dy)/(dt)= t/(t^2y+y),y(0)=-9	\frac{dy}{dt}=\frac{t}{t^{2}y+y},y(0)=-9
(\partial)/(\partial z)(x^2-xyz)	\frac{\partial\:}{\partial\:z}(x^{2}-xyz)
y^{''}-y^'-42y=0	y^{\prime\:\prime\:}-y^{\prime\:}-42y=0
derivative of (3x+2^x)	\frac{d}{dx}((3x+2)^{x})
y^{''}+y^'+4y=0	y^{\prime\:\prime\:}+y^{\prime\:}+4y=0
derivative of 6sqrt(x)sin(x)	derivative\:6\sqrt{x}\sin(x)
(\partial)/(\partial y)(x^{x/y}cos(x/y))	\frac{\partial\:}{\partial\:y}(x^{\frac{x}{y}}\cos(\frac{x}{y}))
((4-x^{2/3})^{3/2})^'	((4-x^{\frac{2}{3}})^{\frac{3}{2}})^{\prime\:}
derivative of f(x)=(1+2x)/(3+x)	derivative\:f(x)=\frac{1+2x}{3+x}
f(x)=(x-1)e^{x^2-4}	f(x)=(x-1)e^{x^{2}-4}
implicit (dy)/(dx),xy-4x=5	implicit\:\frac{dy}{dx},xy-4x=5

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