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Popular Calculus Problems

integral from 0 to 1 of 5^{-θ}	\int\:_{0}^{1}5^{-θ}dθ
(dy)/(dx)=-2xy^2	\frac{dy}{dx}=-2xy^{2}
(dy}{dx}=\frac{x^8-4y)/x	\frac{dy}{dx}=\frac{x^{8}-4y}{x}
integral of (1-ax)^{1/2}	\int\:(1-ax)^{\frac{1}{2}}dx
integral of sin(2t)e^t	\int\:\sin(2t)e^{t}dt
derivative of sin(4sqrt(1-2x^3))	\frac{d}{dx}(\sin(4\sqrt{1-2x^{3}}))
integral of ((ln(x)))/x	\int\:\frac{(\ln(x))}{x}dx
integral of 1/((x+2)^2(x-1))	\int\:\frac{1}{(x+2)^{2}(x-1)}dx
limit as x approaches 0 of (arcsin(3x))/x	\lim\:_{x\to\:0}(\frac{\arcsin(3x)}{x})
derivative of x^{1/2}(2x^{1/2}-1)	derivative\:x^{\frac{1}{2}}(2x^{\frac{1}{2}}-1)
area-1/5 x^2-6/5 x+7/5 ,[-5,5]	area\:-\frac{1}{5}x^{2}-\frac{6}{5}x+\frac{7}{5},[-5,5]
y^'=24.5-(7y)/((280-2x))	y^{\prime\:}=24.5-\frac{7y}{(280-2x)}
integral of 1/x+2	\int\:\frac{1}{x}+2dx
integral of (x^3)/(\sqrt[9]{x^2+7)}	\int\:\frac{x^{3}}{\sqrt[9]{x^{2}+7}}dx
derivative of sqrt(x)e^x	derivative\:\sqrt{x}e^{x}
derivative of e^{x^2*\sqrt[3]{4x-1}}	\frac{d}{dx}(e^{x^{2}\cdot\:\sqrt[3]{4x-1}})
integral of (2x+1)/(2x)	\int\:\frac{2x+1}{2x}dx
integral of (6x^4-5x^3+4x^2)/(2x^2-x+1)	\int\:\frac{6x^{4}-5x^{3}+4x^{2}}{2x^{2}-x+1}dx
integral of (5x^3-3\sqrt[5]{x})/(5x)	\int\:\frac{5x^{3}-3\sqrt[5]{x}}{5x}dx
tangent of g(x)=2-x^3	tangent\:g(x)=2-x^{3}
integral of (x^3+8)/(x+2)	\int\:\frac{x^{3}+8}{x+2}dx
integral of-t^{3/2}	\int\:-t^{\frac{3}{2}}dt
derivative of 10e^x	derivative\:10e^{x}
integral from 2 to 3 of x/(x^2-1)	\int\:_{2}^{3}\frac{x}{x^{2}-1}dx
integral of (ln(x))/(1+x^2)	\int\:\frac{\ln(x)}{1+x^{2}}dx
integral of ln(x/(x+2))	\int\:\ln(\frac{x}{x+2})dx
derivative of x^5-4x^3+x-1	\frac{d}{dx}(x^{5}-4x^{3}+x-1)
24y^{'''}+2y^{''}-5y^'-y=0	24y^{\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}-5y^{\prime\:}-y=0
integral of-cos^4(x)	\int\:-\cos^{4}(x)dx
tangent of f(x)=6x^2-4x+5	tangent\:f(x)=6x^{2}-4x+5
integral of (2\sqrt[3]{x^5})/3	\int\:\frac{2\sqrt[3]{x^{5}}}{3}dx
limit as x approaches 1-of sqrt(3-3x)	\lim\:_{x\to\:1-}(\sqrt{3-3x})
integral of 5/(x^2+36)	\int\:\frac{5}{x^{2}+36}dx
integral of 2^{-x}	\int\:2^{-x}dx
integral from 1 to 5 of sqrt(17)	\int\:_{1}^{5}\sqrt{17}dx
y^'=e^{-y}	y^{\prime\:}=e^{-y}
derivative of arctan(6x)	\frac{d}{dx}(\arctan(6x))
integral from 0 to pi of (8e^x+5sin(x))	\int\:_{0}^{π}(8e^{x}+5\sin(x))dx
integral from 1 to 2 of 4r^4ln(r)	\int\:_{1}^{2}4r^{4}\ln(r)dr
tangent of y=2sqrt(x)+1	tangent\:y=2\sqrt{x}+1
y^'+3/x y=0,y(1)=5	y^{\prime\:}+\frac{3}{x}y=0,y(1)=5
derivative of f(x)=e^xsqrt(1+x^2)	derivative\:f(x)=e^{x}\sqrt{1+x^{2}}
derivative of ln(x^2+2-y)	\frac{d}{dx}(\ln(x^{2}+2-y))
(\partial)/(\partial x)(x/(sin(2x)+3y+z^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sin(2x)+3y+z^{2}})
integral of sinh^3(x)	\int\:\sinh^{3}(x)dx
limit as x approaches 0 of \|x+2\|	\lim\:_{x\to\:0}(\left\|x+2\right\|)
integral of sin^4(x/3)cos(x/3)	\int\:\sin^{4}(\frac{x}{3})\cos(\frac{x}{3})dx
implicit y^5=x^6	implicit\:y^{5}=x^{6}
derivative of (-0.4/(sqrt(5+5x)))	\frac{d}{dx}(\frac{-0.4}{\sqrt{5+5x}})
(dy)/(dx)+0.1y=10	\frac{dy}{dx}+0.1y=10
integral from 1 to 2 of (3^{ln(x)})/x	\int\:_{1}^{2}\frac{3^{\ln(x)}}{x}dx
integral of 2^{3x}	\int\:2^{3x}dx
limit as x approaches 0 of (1+8x)^{5/x}	\lim\:_{x\to\:0}((1+8x)^{\frac{5}{x}})
(d^2)/(d{r)(θ)dθ}({r}(θ)sin(θ))	\frac{d^{2}}{d{r}(θ)dθ}({r}(θ)\sin(θ))
derivative of cos(x^2)-2x^2sin(x^2)	derivative\:\cos(x^{2})-2x^{2}\sin(x^{2})
area \sqrt[6]{x},x^2	area\:\sqrt[6]{x},x^{2}
integral of 8e^{-8x}	\int\:8e^{-8x}dx
d/(dt)(-sin(t))	\frac{d}{dt}(-\sin(t))
tangent of f(x)= 1/(sqrt(1x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{1x}},\at\:x=9
limit as x approaches 4 of (2x+3)/(9x+7)	\lim\:_{x\to\:4}(\frac{2x+3}{9x+7})
integral from 0 to 1 of 1/(x^2-3x+2)	\int\:_{0}^{1}\frac{1}{x^{2}-3x+2}dx
integral from-2 to 4 of (10+4x-3x^3)	\int\:_{-2}^{4}(10+4x-3x^{3})dx
tangent of f(x)=x^3-3x+1,\at x=3	tangent\:f(x)=x^{3}-3x+1,\at\:x=3
derivative of 3/((2x+3)^2)	derivative\:\frac{3}{(2x+3)^{2}}
limit as x approaches infinity of-1^{-x}	\lim\:_{x\to\:\infty\:}(-1^{-x})
derivative of ((x^2-3x+2)/(x^7-2))	\frac{d}{dx}(\frac{(x^{2}-3x+2)}{x^{7}-2})
derivative of (3x-9/(2x+8))	\frac{d}{dx}(\frac{3x-9}{2x+8})
integral from 0 to pi/6 of sec^2(x)	\int\:_{0}^{\frac{π}{6}}\sec^{2}(x)dx
tangent of f(x)=x^3+2x	tangent\:f(x)=x^{3}+2x
(\partial)/(\partial x)(xe^{xy}+x/(y^2))	\frac{\partial\:}{\partial\:x}(xe^{xy}+\frac{x}{y^{2}})
tangent of f(x)=sqrt(x),\at x=64	tangent\:f(x)=\sqrt{x},\at\:x=64
4xyy^'=4y^2+3xsqrt(x^2+y^2)	4xyy^{\prime\:}=4y^{2}+3x\sqrt{x^{2}+y^{2}}
integral of (5/x+(12)/(x^5))	\int\:(\frac{5}{x}+\frac{12}{x^{5}})dx
derivative of f(x)=sqrt(x)(x-1)	derivative\:f(x)=\sqrt{x}(x-1)
integral of (x^2)/((49-x^2)^{3/2)}	\int\:\frac{x^{2}}{(49-x^{2})^{\frac{3}{2}}}dx
integral of 1/((4-2x)^{7/2)}	\int\:\frac{1}{(4-2x)^{\frac{7}{2}}}dx
integral from-1 to 3 of-x^3	\int\:_{-1}^{3}-x^{3}dx
derivative of (2x(sin(x))/(x^3-1))	\frac{d}{dx}(\frac{2x(\sin(x))}{x^{3}-1})
integral of 2/(9+x^2)	\int\:\frac{2}{9+x^{2}}dx
derivative of y=x+5/x	derivative\:y=x+\frac{5}{x}
derivative of-(36/(x^4))	\frac{d}{dx}(-\frac{36}{x^{4}})
derivative of ln(3x-e^{-2x})	\frac{d}{dx}(\ln(3x)-e^{-2x})
integral of (cot(bx)+tan(bx))^2	\int\:(\cot(bx)+\tan(bx))^{2}dx
tangent of f(x)=x^2,\at x=2x-1	tangent\:f(x)=x^{2},\at\:x=2x-1
d/(dy)(sqrt(1-y^2))	\frac{d}{dy}(\sqrt{1-y^{2}})
area y=x^{1/2},x=0,x=1	area\:y=x^{\frac{1}{2}},x=0,x=1
sum from n=1 to infinity of 5/(e^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{5}{e^{2n}}
derivative of (xy)/(x+y)	derivative\:\frac{xy}{x+y}
integral of+x^2*+sin(x)	\int\:+x^{2}\cdot\:+\sin(x)dx
x^{''}-3x^'=e^{3t}	x^{\prime\:\prime\:}-3x^{\prime\:}=e^{3t}
area 2cos(x),4-2cos(x)	area\:2\cos(x),4-2\cos(x)
integral of sin(yz)	\int\:\sin(yz)dy
derivative of ln^2(sqrt(x))	\frac{d}{dx}(\ln^{2}(\sqrt{x}))
derivative of f(x)=-7/(x^8)	derivative\:f(x)=-\frac{7}{x^{8}}
derivative of (x+y^3)	\frac{d}{dx}((x+y)^{3})
derivative of sqrt(2-6x)	derivative\:\sqrt{2-6x}
limit as x approaches 2+of x^2-1	\lim\:_{x\to\:2+}(x^{2}-1)
derivative of sin^2(3x+1)	\frac{d}{dx}(\sin^{2}(3x+1))
limit as x approaches 3 of (x-3)ln(x-3)	\lim\:_{x\to\:3}((x-3)\ln(x-3))
integral of e^{-x/(yln(2))}	\int\:e^{-\frac{x}{y\ln(2)}}dx

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