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Popular Calculus Problems

integral of ((x^2+5x+4))/(x^2-2x+1)	\int\:\frac{(x^{2}+5x+4)}{x^{2}-2x+1}dx
area y=x,y=5x-x^2	area\:y=x,y=5x-x^{2}
derivative of-2+2(-1^x)	\frac{d}{dx}(-2+2(-1)^{x})
derivative of (-2nx^{n-1})/((1+x^n)^2)	derivative\:\frac{-2nx^{n-1}}{(1+x^{n})^{2}}
derivative of (dy/(dx))=y	\frac{d}{dx}(\frac{dy}{dx})=y
integral of e^{-15x}	\int\:e^{-15x}dx
integral of (sqrt(n)+3)^3	\int\:(\sqrt{n}+3)^{3}dn
tangent of y^3=126-x^3,\at x=5	tangent\:y^{3}=126-x^{3},\at\:x=5
y^{''}-12y^'+100y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+100y=0
y^'=5y+e^{-2x}y^{-2},y(0)=2	y^{\prime\:}=5y+e^{-2x}y^{-2},y(0)=2
derivative of f(x)=x^{10}e^x	derivative\:f(x)=x^{10}e^{x}
derivative of 3^{(x^5)}	derivative\:3^{(x^{5})}
sum from n=0 to infinity of sqrt(1+n)	\sum\:_{n=0}^{\infty\:}\sqrt{1+n}
y^'+2y=4,y(0)=4	y^{\prime\:}+2y=4,y(0)=4
derivative of 1/2 tan(x)	\frac{d}{dx}(\frac{1}{2}\tan(x))
integral from 6 to 8 of (50)/((x-6)^3)	\int\:_{6}^{8}\frac{50}{(x-6)^{3}}dx
integral of sqrt((6+x)/(6-x))	\int\:\sqrt{\frac{6+x}{6-x}}dx
integral of x^{4n}	\int\:x^{4n}dx
tangent of f(x)=(2x-1)/(x+1),\at x=1	tangent\:f(x)=\frac{2x-1}{x+1},\at\:x=1
derivative of (6x+x^2/((3+x)^2))	\frac{d}{dx}(\frac{6x+x^{2}}{(3+x)^{2}})
limit as n approaches infinity of 0.5^n	\lim\:_{n\to\:\infty\:}(0.5^{n})
derivative of 6sqrt(xe^x)	derivative\:6\sqrt{xe^{x}}
inverse oflaplace ((3s+2))/((s^2+4s+20))	inverselaplace\:\frac{(3s+2)}{(s^{2}+4s+20)}
limit as x approaches 0+of x/(1+ln(x))	\lim\:_{x\to\:0+}(\frac{x}{1+\ln(x)})
y^{''}+7y^'=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+7y^{\prime\:}=0,y(0)=1,y^{\prime\:}(0)=1
(dy)/(dx)=2yx+yx^2,y(-3)=1	\frac{dy}{dx}=2yx+yx^{2},y(-3)=1
tangent of h(x)= 1/(2sqrt(x)),\at x=4	tangent\:h(x)=\frac{1}{2\sqrt{x}},\at\:x=4
limit as x approaches-2 of 2x^2	\lim\:_{x\to\:-2}(2x^{2})
integral of x^3sqrt(5+x^2)	\int\:x^{3}\sqrt{5+x^{2}}dx
derivative of sqrt(x+7)	derivative\:\sqrt{x+7}
integral from 0 to 4 of sqrt(1+36x)	\int\:_{0}^{4}\sqrt{1+36x}dx
integral from-1 to 2 of (2-x^2+x)	\int\:_{-1}^{2}(2-x^{2}+x)dx
limit as x approaches 0 of xcos((11)/x)	\lim\:_{x\to\:0}(x\cos(\frac{11}{x}))
derivative of f(x)=-8/(x^3)	derivative\:f(x)=-\frac{8}{x^{3}}
(dy)/(dx)=sqrt(x)y	\frac{dy}{dx}=\sqrt{x}y
derivative of f(x)= 4/3 pix^2	derivative\:f(x)=\frac{4}{3}πx^{2}
(\partial)/(\partial y)((x-y)^2y)	\frac{\partial\:}{\partial\:y}((x-y)^{2}y)
(\partial)/(\partial x)(3arctan(x/y))	\frac{\partial\:}{\partial\:x}(3\arctan(\frac{x}{y}))
y^{''}-8y^'+15y=-sin(2t)	y^{\prime\:\prime\:}-8y^{\prime\:}+15y=-\sin(2t)
y^{''}-2y^'+26y=e^xsin(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+26y=e^{x}\sin(x)
(\partial)/(\partial x)(e^{2x+8y})	\frac{\partial\:}{\partial\:x}(e^{2x+8y})
tangent of 8sqrt(x)	tangent\:8\sqrt{x}
(\partial)/(\partial x)(2y^3)	\frac{\partial\:}{\partial\:x}(2y^{3})
derivative of (5x-3)^4(2x-7)^{-3}	derivative\:(5x-3)^{4}(2x-7)^{-3}
derivative of (3x^2/(sqrt(x)))	\frac{d}{dx}(\frac{3x^{2}}{\sqrt{x}})
derivative of-0.4x^3	\frac{d}{dx}(-0.4x^{3})
limit as x approaches 0 of 5/4 pi-pi	\lim\:_{x\to\:0}(\frac{5}{4}π-π)
limit as x approaches 0 of 1/(2-e^{1/x)}	\lim\:_{x\to\:0}(\frac{1}{2-e^{\frac{1}{x}}})
integral from 1/2 to 1 of (x^{-3}-3)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-3)dx
limit as x approaches 2 of x^3+2x^2+1	\lim\:_{x\to\:2}(x^{3}+2x^{2}+1)
implicit (dy)/(dx),x^3-3xy^2+y^3=1	implicit\:\frac{dy}{dx},x^{3}-3xy^{2}+y^{3}=1
y^'=3x+y,y(0)=5	y^{\prime\:}=3x+y,y(0)=5
tangent of y=2sqrt(x),(1,2)	tangent\:y=2\sqrt{x},(1,2)
integral of 1/((x)ln(x))	\int\:\frac{1}{(x)\ln(x)}dx
derivative of ((x^2)/(x^2+4))	\frac{d}{dx}(\frac{(x^{2})}{x^{2}+4})
sum from n=0 to infinity of-6(1/4)^{2n}	\sum\:_{n=0}^{\infty\:}-6(\frac{1}{4})^{2n}
integral from 0 to 1 of (2x)/((x^2+3)^3)	\int\:_{0}^{1}\frac{2x}{(x^{2}+3)^{3}}dx
limit as x approaches infinity of ((e^{x^4-x^2}))/2	\lim\:_{x\to\:\infty\:}(\frac{(e^{x^{4}-x^{2}})}{2})
derivative of f(x)=xsqrt(1+x^2)	derivative\:f(x)=x\sqrt{1+x^{2}}
integral of (e^{-2x})/(1+e^{-x)}	\int\:\frac{e^{-2x}}{1+e^{-x}}dx
(\partial)/(\partial x)(3x^2-2xy+x-3y)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy+x-3y)
sum from n=0 to infinity of 1/(n^2+3)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+3}
limit as x approaches 1 of-x^2	\lim\:_{x\to\:1}(-x^{2})
derivative of 2/(2-x)	\frac{d}{dx}(\frac{2}{2-x})
integral of ((x^2))/(x^2+1)	\int\:\frac{(x^{2})}{x^{2}+1}dx
derivative of 5-2(x-2^2)	\frac{d}{dx}(5-2(x-2)^{2})
d/(dy)(yx)	\frac{d}{dy}(yx)
(\partial)/(\partial t)(cos(t)-sin(t))	\frac{\partial\:}{\partial\:t}(\cos(t)-\sin(t))
(\partial)/(\partial x)((x+y)/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{1+x^{2}})
(d^4)/(dx^4)(1/(1-x))	\frac{d^{4}}{dx^{4}}(\frac{1}{1-x})
d/(dt)(t+3)	\frac{d}{dt}(t+3)
(\partial)/(\partial y)(sqrt(7-x^2-2y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{7-x^{2}-2y^{2}})
tangent of f(x)=x^3,\at x=-3	tangent\:f(x)=x^{3},\at\:x=-3
limit as x approaches-2 of x-2	\lim\:_{x\to\:-2}(x-2)
derivative of 2+x	\frac{d}{dx}(2+x)
integral of e^{-1/2}	\int\:e^{-\frac{1}{2}}dx
implicit (dy)/(dx),y^5=x^6	implicit\:\frac{dy}{dx},y^{5}=x^{6}
2y^'+y=3t^2	2y^{\prime\:}+y=3t^{2}
y^{''}-y=2xe^x	y^{\prime\:\prime\:}-y=2xe^{x}
(\partial)/(\partial v)(sqrt(u/v))	\frac{\partial\:}{\partial\:v}(\sqrt{\frac{u}{v}})
derivative of 5+x	\frac{d}{dx}(5+x)
laplacetransform 1/2 (e^x+e^{-x})	laplacetransform\:\frac{1}{2}(e^{x}+e^{-x})
integral of sin(x+y)	\int\:\sin(x+y)dx
derivative of (x+1/(x+3))	\frac{d}{dx}(\frac{x+1}{x+3})
f(x)=(4x+4)/(3x^{2/3)}	f(x)=\frac{4x+4}{3x^{\frac{2}{3}}}
integral from-1 to 4 of 2-2x	\int\:_{-1}^{4}2-2xdx
derivative of cos^3(pix)	derivative\:\cos^{3}(πx)
x^2(dy)/(dx)=2xy+y^2	x^{2}\frac{dy}{dx}=2xy+y^{2}
limit as x approaches 2 of ((3))/(x+2)	\lim\:_{x\to\:2}(\frac{(3)}{x+2})
(\partial)/(\partial x)(-7xy)	\frac{\partial\:}{\partial\:x}(-7xy)
derivative of sin(6)	\frac{d}{dx}(\sin(6))
integral from 1 to t of 7x^{-3}	\int\:_{1}^{t}7x^{-3}dx
(x^2+2y^2)=xyy^',y(-1)=1	(x^{2}+2y^{2})=xyy^{\prime\:},y(-1)=1
integral from 3 to infinity of 4/(x^2-x)	\int\:_{3}^{\infty\:}\frac{4}{x^{2}-x}dx
integral of 8xln(2x)	\int\:8x\ln(2x)dx
limit as x approaches 1 of x^2+x-3	\lim\:_{x\to\:1}(x^{2}+x-3)
tangent of f(x)=x^3+2x,\at x=-3	tangent\:f(x)=x^{3}+2x,\at\:x=-3
sum from n=1 to infinity of (1/n)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{n})^{n}
integral from 0 to 2 of (x^2-5x)	\int\:_{0}^{2}(x^{2}-5x)dx
derivative of 4\sqrt[3]{x}	\frac{d}{dx}(4\sqrt[3]{x})

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