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Popular Calculus Problems

integral from 0 to 5 of (x/(sqrt(x+4)))	\int\:_{0}^{5}(\frac{x}{\sqrt{x+4}})dx
y^'+y+1=0	y^{\prime\:}+y+1=0
derivative of (1+xcos(x))	\frac{d}{dx}((1+x)\cos(x))
derivative of f(t)=cos^2(e^{cos^2(t)})	derivative\:f(t)=\cos^{2}(e^{\cos^{2}(t)})
integral of (19)/(x^2+1)	\int\:\frac{19}{x^{2}+1}dx
(\partial)/(\partial x)(7e^x)	\frac{\partial\:}{\partial\:x}(7e^{x})
integral of x/(x-2)	\int\:\frac{x}{x-2}dx
y^'=(x-2)/(y+1)	y^{\prime\:}=\frac{x-2}{y+1}
integral of-\|x\|^2	\int\:-\left\|x\right\|^{2}dx
integral from 0 to 1 of 4ln(x)	\int\:_{0}^{1}4\ln(x)dx
derivative of (sin^2(x)/2)	\frac{d}{dx}(\frac{\sin^{2}(x)}{2})
slope derivative of 5/(4x)-7/4	slope\:\frac{d}{dx}(\frac{5}{4x})-\frac{7}{4}
integral of ((arctan(x))^3)/(1+x^2)	\int\:\frac{(\arctan(x))^{3}}{1+x^{2}}dx
(\partial)/(\partial x)(x/(x^2+(y-1)^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+(y-1)^{2}})
integral of 1/(12x)	\int\:\frac{1}{12x}dx
derivative of log_{5}(x^2-7x)	\frac{d}{dx}(\log_{5}(x^{2}-7x))
v'=-0.01v^2	v\prime\:=-0.01v^{2}
y^{''}+2y^'+2y=sin(1t)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(1t)
limit as x approaches 5 of-2	\lim\:_{x\to\:5}(-2)
inverse oflaplace 6/((s-2)^4)	inverselaplace\:\frac{6}{(s-2)^{4}}
derivative of f(x)=x^2+8	derivative\:f(x)=x^{2}+8
integral of 4x^{1/3}-4x^{-1/3}	\int\:4x^{\frac{1}{3}}-4x^{-\frac{1}{3}}dx
integral of-(sin(x))^2	\int\:-(\sin(x))^{2}dx
f(t)=2sin^2(t)	f(t)=2\sin^{2}(t)
integral from-pi to pi of cos^2(5x)	\int\:_{-π}^{π}\cos^{2}(5x)dx
limit as x approaches pi/2+of 1/x sec(x)	\lim\:_{x\to\:\frac{π}{2}+}(\frac{1}{x}\sec(x))
integral of sec(38w)tan(38w)	\int\:\sec(38w)\tan(38w)dw
limit as x approaches 1 of \|x-2\|	\lim\:_{x\to\:1}(\left\|x-2\right\|)
integral of tan(x)sec^3(x)	\int\:\tan(x)\sec^{3}(x)dx
integral of x/(x+	\int\:\frac{x}{x+d}dx
(\partial)/(\partial x)(x^3-2xy+y^2+3)	\frac{\partial\:}{\partial\:x}(x^{3}-2xy+y^{2}+3)
y^{'''}=0	y^{\prime\:\prime\:\prime\:}=0
inverse oflaplace 4/(5s)	inverselaplace\:\frac{4}{5s}
integral of (\sqrt[6]{x}+\sqrt[7]{x})	\int\:(\sqrt[6]{x}+\sqrt[7]{x})dx
4y^{''}+12y^'+9y=0,y(0)=1,y^'(0)=-5	4y^{\prime\:\prime\:}+12y^{\prime\:}+9y=0,y(0)=1,y^{\prime\:}(0)=-5
derivative of sqrt(x)sin(x)	derivative\:\sqrt{x}\sin(x)
derivative of f(x)=sqrt(1+8x)	derivative\:f(x)=\sqrt{1+8x}
derivative of (1+x^4)^{2/3}	derivative\:(1+x^{4})^{\frac{2}{3}}
derivative of ((5x-3)/((4x-3/x)))	\frac{d}{dx}(\frac{(5x-3)}{(4x-\frac{3}{x})})
(\partial)/(\partial x)(y(-14x-4y+1))	\frac{\partial\:}{\partial\:x}(y(-14x-4y+1))
integral of x(x^2+3)^2	\int\:x(x^{2}+3)^{2}dx
integral of 2/(x^{1/2)}	\int\:\frac{2}{x^{\frac{1}{2}}}dx
2x+3y+(6x+9y-3)y^'=0	2x+3y+(6x+9y-3)y^{\prime\:}=0
derivative of f(x)=cos(x^2)-2x^2sin(x^2)	derivative\:f(x)=\cos(x^{2})-2x^{2}\sin(x^{2})
(\partial)/(\partial y)((x+y)(x-y))	\frac{\partial\:}{\partial\:y}((x+y)(x-y))
derivative of tan^{40}(sec(cos(x)))	\frac{d}{dx}(\tan^{40}(\sec(\cos(x))))
derivative of x^e+1/(x^{sqrt(10)})	\frac{d}{dx}(x^{e}+\frac{1}{x^{\sqrt{10}}})
derivative of-x/(8y)	derivative\:-\frac{x}{8y}
(d^2)/(dx^2)((4x^2+8x)cos(x))	\frac{d^{2}}{dx^{2}}((4x^{2}+8x)\cos(x))
inverse oflaplace a/(s^2+a^2)	inverselaplace\:\frac{a}{s^{2}+a^{2}}
(x^2)/(y^2-2)(dy)/(dx)= 1/(2y)	\frac{x^{2}}{y^{2}-2}\frac{dy}{dx}=\frac{1}{2y}
integral from-10 to 10 of (x^2+x)	\int\:_{-10}^{10}(x^{2}+x)dx
derivative of x(1-2x^3)	\frac{d}{dx}(x(1-2x)^{3})
tangent of f(x)=8x-3x^2	tangent\:f(x)=8x-3x^{2}
integral from-1 to 2 of 1/(x^5)	\int\:_{-1}^{2}\frac{1}{x^{5}}dx
derivative of-4/(x^3)	derivative\:-\frac{4}{x^{3}}
integral of 2(x+y)	\int\:2(x+y)dx
(d^2)/(dx^2)(xsin(x))	\frac{d^{2}}{dx^{2}}(x\sin(x))
(\partial)/(\partial x)(cos(y^2-2x))	\frac{\partial\:}{\partial\:x}(\cos(y^{2}-2x))
derivative of (x+1)/(x-1)	derivative\:\frac{x+1}{x-1}
derivative of t^5ln\|t\|	derivative\:t^{5}\ln\left\|t\right\|
(\partial)/(\partial x)(log_{10}(xy))	\frac{\partial\:}{\partial\:x}(\log_{10}(xy))
area y=x^2-2x,y=-x^2+4x	area\:y=x^{2}-2x,y=-x^{2}+4x
limit as x approaches 2+of 3/(x^2-4)	\lim\:_{x\to\:2+}(\frac{3}{x^{2}-4})
sum from n=1 to infinity of 1/(n^4+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{4}+1}
derivative of sqrt(r)+\sqrt[5]{r}	derivative\:\sqrt{r}+\sqrt[5]{r}
integral of sqrt(1+x^{-2/3)}	\int\:\sqrt{1+x^{-\frac{2}{3}}}dx
(\partial)/(\partial x)(1/(x+4y))	\frac{\partial\:}{\partial\:x}(\frac{1}{x+4y})
integral of 28t(7t^2-5)^3	\int\:28t(7t^{2}-5)^{3}dt
(\partial)/(\partial y)((2x)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{2x}{x^{2}+y^{2}})
integral of (x^2)/((16+x^2)^2)	\int\:\frac{x^{2}}{(16+x^{2})^{2}}dx
integral of (8x-7)*ln(x)	\int\:(8x-7)\cdot\:\ln(x)dx
area xsqrt(8-2x^2),0,2	area\:x\sqrt{8-2x^{2}},0,2
derivative of \sqrt[4]{(4x)/(4x-3)}	derivative\:\sqrt[4]{\frac{4x}{4x-3}}
(\partial)/(\partial x)(ln(x/y))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{y}))
integral from-a to a of e^{(-x^2)/(a^2)}	\int\:_{-a}^{a}e^{\frac{-x^{2}}{a^{2}}}dx
slope of (-4,3),(3,1)	slope\:(-4,3),(3,1)
integral of (x^2-15)/(x+7)	\int\:\frac{x^{2}-15}{x+7}dx
y^{''}-2y^'=9x	y^{\prime\:\prime\:}-2y^{\prime\:}=9x
integral from 0 to 2 of (3x^2-2)	\int\:_{0}^{2}(3x^{2}-2)dx
derivative of (2+u^2)^5(5-9u^2)^8	derivative\:(2+u^{2})^{5}(5-9u^{2})^{8}
integral of 3x(7-x)	\int\:3x(7-x)dx
tangent of f(x)=5+4x^2-2x^3,(1,7)	tangent\:f(x)=5+4x^{2}-2x^{3},(1,7)
integral of ((3x^2-4)^{3/2}4x^3)/(x^2)	\int\:\frac{(3x^{2}-4)^{\frac{3}{2}}4x^{3}}{x^{2}}dx
derivative of (sin(x)/(1+cos(x)))	\frac{d}{dx}(\frac{\sin(x)}{1+\cos(x)})
integral of e^{-st}tcos(t)	\int\:e^{-st}t\cos(t)dt
inverse oflaplace 5/(s(s^2+s+1))	inverselaplace\:\frac{5}{s(s^{2}+s+1)}
integral from-2 to 2 of 4^x	\int\:_{-2}^{2}4^{x}dx
((dy))/((dx))=8x^{(3)}+6x^{(2)}	\frac{(dy)}{(dx)}=8x^{(3)}+6x^{(2)}
derivative of sqrt(15x)ln(4x)	derivative\:\sqrt{15x}\ln(4x)
integral of 8/(5^{3x)}	\int\:\frac{8}{5^{3x}}dx
integral of (x^2+12x+12)/(x(x^2-4))	\int\:\frac{x^{2}+12x+12}{x(x^{2}-4)}dx
derivative of (8x^2+6x+6/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+6x+6}{\sqrt{x}})
integral of 16sin^2(xco)s^2x	\int\:16\sin^{2}(xco)s^{2}xdx
y^{''}+4y=sec^2(2x)	y^{\prime\:\prime\:}+4y=\sec^{2}(2x)
integral of 5tan^3(θ)	\int\:5\tan^{3}(θ)dθ
inverse oflaplace 1/(s^2+s+1)	inverselaplace\:\frac{1}{s^{2}+s+1}
integral of sin^2(1/2 x)	\int\:\sin^{2}(\frac{1}{2}x)dx
derivative of 9x^4	\frac{d}{dx}(9x^{4})
integral of x/(2-3x)	\int\:\frac{x}{2-3x}dx

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