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Popular Calculus Problems

integral of 7e^xsqrt(2+e^x)	\int\:7e^{x}\sqrt{2+e^{x}}dx
derivative of-1/4 sin(x/2)	\frac{d}{dx}(-\frac{1}{4}\sin(\frac{x}{2}))
y=2xy^'	y=2xy^{\prime\:}
expand (x+1)(x^3+x-2)	expand\:(x+1)(x^{3}+x-2)
y^'-(6y)/x =(y/(x^2))^4	y^{\prime\:}-\frac{6y}{x}=(\frac{y}{x^{2}})^{4}
integral of ((sqrt(x)+3)^4)/(sqrt(x))	\int\:\frac{(\sqrt{x}+3)^{4}}{\sqrt{x}}dx
derivative of (x+1(x+1-1/(x+2)))	\frac{d}{dx}((x+1)(x+1-\frac{1}{x+2}))
integral of 1/(sqrt(5-8x-x^2))	\int\:\frac{1}{\sqrt{5-8x-x^{2}}}dx
integral of (e^{3x}+e^{-3x})^2	\int\:(e^{3x}+e^{-3x})^{2}dx
derivative of ln(sqrt(4-3x^3))	\frac{d}{dx}(\ln(\sqrt{4-3x^{3}}))
derivative of (-2x)/((x^2+1)^2)	derivative\:\frac{-2x}{(x^{2}+1)^{2}}
ty^'+2y=t^2-t+1	t\cdot\:y^{\prime\:}+2\cdot\:y=t^{2}-t+1
derivative of f(x)=e^{-3x}sin(4x^2)	derivative\:f(x)=e^{-3x}\sin(4x^{2})
integral of e^{9-4x}	\int\:e^{9-4x}dx
integral of (cos(x))/(3+2sin(x))	\int\:\frac{\cos(x)}{3+2\sin(x)}dx
derivative of y=6x(x^2+2)2	derivative\:y=6x(x^{2}+2)2
integral of ((3x+11))/(x^2-x-6)	\int\:\frac{(3x+11)}{x^{2}-x-6}dx
derivative of sqrt(x+11)	derivative\:\sqrt{x+11}
tangent of f(x)=(4x)/(x+2),\at x=2	tangent\:f(x)=\frac{4x}{x+2},\at\:x=2
(\partial)/(\partial x)((y^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{y^{2}}{x^{2}+y^{2}})
area x^3-11x^2+18x,-x^3+11x^2-18x	area\:x^{3}-11x^{2}+18x,-x^{3}+11x^{2}-18x
integral of (-ln(x))/2	\int\:\frac{-\ln(x)}{2}dx
f(x)=x^2sqrt(1-x^2)	f(x)=x^{2}\sqrt{1-x^{2}}
derivative of f(x)=x^3-3x+5	derivative\:f(x)=x^{3}-3x+5
derivative of f(x)=(cos(x)+4)/(1-sin(x))	derivative\:f(x)=\frac{\cos(x)+4}{1-\sin(x)}
integral of 1/(C^2)	\int\:\frac{1}{C^{2}}dC
tangent of f(x)=2\sqrt[3]{x},\at x=8	tangent\:f(x)=2\sqrt[3]{x},\at\:x=8
(dx)/(dt)=((e^t-e^{-t}))/(3+x)	\frac{dx}{dt}=\frac{(e^{t}-e^{-t})}{3+x}
y^'+1/x y=10x^2	y^{\prime\:}+\frac{1}{x}y=10x^{2}
derivative of sqrt(1-sin(x))	\frac{d}{dx}(\sqrt{1-\sin(x)})
derivative of 6x-5	\frac{d}{dx}(6x-5)
derivative of (e^{2x}+e^{-2x}/x)	\frac{d}{dx}(\frac{e^{2x}+e^{-2x}}{x})
derivative of Xsqrt(X+1)	derivative\:X\sqrt{X+1}
integral of (t-3)/(sqrt(t))	\int\:\frac{t-3}{\sqrt{t}}dt
(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)	\frac{\partial\:}{\partial\:x}(y\sqrt{x}-y^{2}-x+3y)
derivative of (9sqrt(x+8))x^2	derivative\:(9\sqrt{x+8})x^{2}
integral from 0 to infinity of (ye^{(-y)/a})/(a)	\int\:_{0}^{\infty\:}\frac{ye^{\frac{-y}{a}}}{a}dy
y^{''}-2y^'+y=2e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=2e^{x}
tangent of f(x)=sin(sin(x)),\at x=2pi	tangent\:f(x)=\sin(\sin(x)),\at\:x=2π
limit as x approaches-1+of arcsin(x)	\lim\:_{x\to\:-1+}(\arcsin(x))
derivative of f(x)=ln((x+3)/(x-3))	derivative\:f(x)=\ln(\frac{x+3}{x-3})
derivative of (4x+5^2)	\frac{d}{dx}((4x+5)^{2})
f(x)=sin(x^3)	f(x)=\sin(x^{3})
slope of (-4,2),(0,4)	slope\:(-4,2),(0,4)
(d^3)/(dx^3)(sqrt(2t+3))	\frac{d^{3}}{dx^{3}}(\sqrt{2t+3})
integral of 1/(sqrt(5-7x-3x^2))	\int\:\frac{1}{\sqrt{5-7x-3x^{2}}}dx
derivative of f(x)=8arcsin(x^3)	derivative\:f(x)=8\arcsin(x^{3})
derivative of f(x)=2x^3-5x^4	derivative\:f(x)=2x^{3}-5x^{4}
integral of y/(e^y)	\int\:\frac{y}{e^{y}}dy
integral from 0 to 1 of pi(e^x)^2	\int\:_{0}^{1}π(e^{x})^{2}dx
area x^2,x^2-4x+4,0,1	area\:x^{2},x^{2}-4x+4,0,1
integral of e^{-r^2}	\int\:e^{-r^{2}}dr
derivative of x^2(x-2(x+4))	\frac{d}{dx}(x^{2}(x-2)(x+4))
integral of e^{-r}	\int\:e^{-r}dr
limit as x approaches 0 of (e^{2x-1})/x	\lim\:_{x\to\:0}(\frac{e^{2x-1}}{x})
integral of 4sqrt(4-x^2)	\int\:4\sqrt{4-x^{2}}dx
integral of (x^2-2)sqrt(x^3-6x+3)	\int\:(x^{2}-2)\sqrt{x^{3}-6x+3}dx
integral of 1/(-v^2)	\int\:\frac{1}{-v^{2}}dv
derivative of log_{2}(x^2+1-2^3)	\frac{d}{dx}(\log_{2}(x^{2}+1)-2^{3})
integral of 3xe^{7x^2}	\int\:3xe^{7x^{2}}dx
limit as x approaches 2-of ln(x-2)	\lim\:_{x\to\:2-}(\ln(x-2))
limit as x approaches 0 of (1+x)^{-1/x}	\lim\:_{x\to\:0}((1+x)^{-\frac{1}{x}})
f(x)=16cos(2x)	f(x)=16\cos(2x)
integral of csc^2(x)	\int\:\csc^{2}(x)dx
area 2x^2+1,-1,6	area\:2x^{2}+1,-1,6
limit as x approaches 0 of 3-sqrt(9+x)	\lim\:_{x\to\:0}(3-\sqrt{9+x})
integral from 0 to 1 of 4x	\int\:_{0}^{1}4xdx
f(x)=tan((pix)/2)	f(x)=\tan(\frac{πx}{2})
derivative of y=(3x-2x^2)3	\frac{d}{dx}y=(3x-2x^{2})3
integral of (9x^2)/((25+x^2)^2)	\int\:\frac{9x^{2}}{(25+x^{2})^{2}}dx
integral from 0 to 6 of x	\int\:_{0}^{6}xdx
integral of 3xe^x	\int\:3xe^{x}dx
limit as x approaches 0 of (3x^2-4x)/x	\lim\:_{x\to\:0}(\frac{3x^{2}-4x}{x})
integral of ln(2x+7)	\int\:\ln(2x+7)dx
derivative of (sin(x)^{tan(x)})	\frac{d}{dx}((\sin(x))^{\tan(x)})
integral from 0 to e of 2piy(1-ln(y))	\int\:_{0}^{e}2πy(1-\ln(y))dy
tangent of 8/(sqrt(x+11)),\at x=5	tangent\:\frac{8}{\sqrt{x+11}},\at\:x=5
sum from n=0 to infinity of (3/7)^{n/2}	\sum\:_{n=0}^{\infty\:}(\frac{3}{7})^{\frac{n}{2}}
integral from-1 to 1 of 1/2 x^3-2x+2	\int\:_{-1}^{1}\frac{1}{2}x^{3}-2x+2dx
integral of 1/(x^3)sin(1/x)	\int\:\frac{1}{x^{3}}\sin(\frac{1}{x})dx
parity \sqrt[4]{1+2x+x^3}	parity\:\sqrt[4]{1+2x+x^{3}}
y^{''}-2y^'-3y=24te^{2t},y(0)=5,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=24te^{2t},y(0)=5,y^{\prime\:}(0)=0
derivative of x(4)	\frac{d}{dx}(x(4))
tangent of y=(4x)/(x+1),(3,3)	tangent\:y=\frac{4x}{x+1},(3,3)
tangent of 6x^2+4x-3	tangent\:6x^{2}+4x-3
integral of (x^{n+1})/(n+1)	\int\:\frac{x^{n+1}}{n+1}dx
derivative of ln^x(x)	\frac{d}{dx}(\ln^{x}(x))
d/(dt)(1/(e^t))	\frac{d}{dt}(\frac{1}{e^{t}})
derivative of f(x)=(1+sqrt(3x))/(1-sqrt(3x))	derivative\:f(x)=\frac{1+\sqrt{3x}}{1-\sqrt{3x}}
integral from 0 to 1 of [x-x^k]	\int\:_{0}^{1}[x-x^{k}]dx
(dy)/(dx)-y/2 = 5/2	\frac{dy}{dx}-\frac{y}{2}=\frac{5}{2}
taylor x/(1-x),0	taylor\:\frac{x}{1-x},0
limit as h approaches 0 of h+2	\lim\:_{h\to\:0}(h+2)
integral of e^{-x/2}cos(3x)	\int\:e^{-\frac{x}{2}}\cos(3x)dx
derivative of F(x)=\sqrt[3]{3+tan(x)}	derivative\:F(x)=\sqrt[3]{3+\tan(x)}
integral of (x^3)/(sqrt(x^2-9))	\int\:\frac{x^{3}}{\sqrt{x^{2}-9}}dx
(\partial)/(\partial y)(6+xln(xy-7))	\frac{\partial\:}{\partial\:y}(6+x\ln(xy-7))
(\partial)/(\partial x)(xy(1-x-y))	\frac{\partial\:}{\partial\:x}(xy(1-x-y))
derivative of 2/(sin(x))	\frac{d}{dx}(\frac{2}{\sin(x)})
taylor sin(2x),0	taylor\:\sin(2x),0

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