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Popular Calculus Problems

integral of x^3*cos(x^4+2)+x^{-1}	\int\:x^{3}\cdot\:\cos(x^{4}+2)+x^{-1}dx
d/(dy)(yln(x))	\frac{d}{dy}(y\ln(x))
integral of 7θsec^2(θ)	\int\:7θ\sec^{2}(θ)dθ
integral of 4x-(x^3)/3	\int\:4x-\frac{x^{3}}{3}dx
integral of (3-2x-4x^2)(1+4x)	\int\:(3-2x-4x^{2})(1+4x)dx
integral of 10xsin(x)	\int\:10x\sin(x)dx
tangent of y=5+4x^2	tangent\:y=5+4x^{2}
(\partial)/(\partial x)(12x^2y^3)	\frac{\partial\:}{\partial\:x}(12x^{2}y^{3})
limit as x approaches 0+of (e^x+x)^{3/x}	\lim\:_{x\to\:0+}((e^{x}+x)^{\frac{3}{x}})
integral of 1/(x^2+2x+3)	\int\:\frac{1}{x^{2}+2x+3}dx
(dy)/(dx)= x/(1+2y)	\frac{dy}{dx}=\frac{x}{1+2y}
tangent of f(x)=(x^3)/3+2x^2+13x-5	tangent\:f(x)=\frac{x^{3}}{3}+2x^{2}+13x-5
sum from n=1 to infinity of n/(ln(2n))	\sum\:_{n=1}^{\infty\:}\frac{n}{\ln(2n)}
tangent of x^3-2x+2,\at x=3,y=21	tangent\:x^{3}-2x+2,\at\:x=3,y=21
(\partial}{\partial x}(\frac{8x+5y)/z)	\frac{\partial\:}{\partial\:x}(\frac{8x+5y}{z})
(\partial)/(\partial x)(2(y/x)^{0.5})	\frac{\partial\:}{\partial\:x}(2(\frac{y}{x})^{0.5})
-y/((x^2+y^2))dx+x/(x^2+y^2)dy=0	-\frac{y}{(x^{2}+y^{2})}dx+\frac{x}{x^{2}+y^{2}}dy=0
integral of (x-1)(x-4)	\int\:(x-1)(x-4)dx
integral of (22)/(xsqrt(1+2x))	\int\:\frac{22}{x\sqrt{1+2x}}dx
(d^2)/(dx^2)(sqrt(r)+\sqrt[9]{r})	\frac{d^{2}}{dx^{2}}(\sqrt{r}+\sqrt[9]{r})
derivative of x+4/(x+3)	\frac{d}{dx}(x+\frac{4}{x+3})
derivative of (tan(x)^x)	\frac{d}{dx}((\tan(x))^{x})
(dy)/(dx)=(cos(6x))/(e^{6y)}	\frac{dy}{dx}=\frac{\cos(6x)}{e^{6y}}
(dy)/(dx)=(3x)/(y+x^2y)	\frac{dy}{dx}=\frac{3x}{y+x^{2}y}
(\partial)/(\partial x)((x-y)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{x^{2}+y^{2}})
integral of (1-x)/(x^2+3x+2)	\int\:\frac{1-x}{x^{2}+3x+2}dx
derivative of xe^xsin(2x)	\frac{d}{dx}(xe^{x}\sin(2x))
integral of (5x^4+3x^3-2)	\int\:(5x^{4}+3x^{3}-2)dx
integral of (sqrt(cos(θ))-2sin(θ))^2	\int\:(\sqrt{\cos(θ)}-2\sin(θ))^{2}dθ
(x-y+2)dx-(x-y)dy=0	(x-y+2)dx-(x-y)dy=0
limit as x approaches 0 of (1+2x)^{5/x}	\lim\:_{x\to\:0}((1+2x)^{\frac{5}{x}})
tangent of 2x^3+2xy+2y^2=38,(-1,-4)	tangent\:2x^{3}+2xy+2y^{2}=38,(-1,-4)
limit as x approaches 0 of (sin(x))/x-1	\lim\:_{x\to\:0}(\frac{\sin(x)}{x}-1)
integral from 2 to 5 of 1/(sqrt(x-2))	\int\:_{2}^{5}\frac{1}{\sqrt{x-2}}dx
derivative of f(x)=(2x^3+5x)(x-3)(x+2)	derivative\:f(x)=(2x^{3}+5x)(x-3)(x+2)
limit as x approaches pi of 3cot(x)	\lim\:_{x\to\:π}(3\cot(x))
integral of (15e^{5r})/(e^{5r)+2}	\int\:\frac{15e^{5r}}{e^{5r}+2}dr
tangent of y=-3cos(x),\at x=(3pi)/4	tangent\:y=-3\cos(x),\at\:x=\frac{3π}{4}
integral of (x+1)^3	\int\:(x+1)^{3}dx
derivative of (2x/(x^2-1))	\frac{d}{dx}(\frac{2x}{x^{2}-1})
limit as x approaches 0-of-x	\lim\:_{x\to\:0-}(-x)
derivative of f(x)=e^{1-x}	derivative\:f(x)=e^{1-x}
(\partial)/(\partial x)(6e^{xy+3})	\frac{\partial\:}{\partial\:x}(6e^{xy+3})
sum from n=0 to infinity of 1/(n^{1/2)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{\frac{1}{2}}}
derivative of (x^2)/(3(2-x))	derivative\:\frac{x^{2}}{3(2-x)}
tangent of y=-2sin(x),\at x=(3pi)/4	tangent\:y=-2\sin(x),\at\:x=\frac{3π}{4}
(dy)/(dx)= 2/(x^2)	\frac{dy}{dx}=\frac{2}{x^{2}}
limit as x approaches 0 of 1/(9-3^{1/x)}	\lim\:_{x\to\:0}(\frac{1}{9-3^{\frac{1}{x}}})
derivative of cos(8θ)	derivative\:\cos(8θ)
(\partial)/(\partial x)(tan(2x)sin(2x))	\frac{\partial\:}{\partial\:x}(\tan(2x)\sin(2x))
derivative of f(x)=sqrt(4x^2-5x)	derivative\:f(x)=\sqrt{4x^{2}-5x}
(\partial)/(\partial z)(cos(xz))	\frac{\partial\:}{\partial\:z}(\cos(xz))
sum from n=1 to infinity of n/(2n^3+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n^{3}+1}
tangent of 2/(sqrt(x)),\at x= 1/9	tangent\:\frac{2}{\sqrt{x}},\at\:x=\frac{1}{9}
derivative of x(2)	\frac{d}{dx}(x(2))
(dy)/(dx)=e^{csc(6x)tan(6x)}	\frac{dy}{dx}=e^{\csc(6x)\tan(6x)}
y^{''}-3y^'+8y=xe^x	y^{\prime\:\prime\:}-3y^{\prime\:}+8y=xe^{x}
y^'+9(tan(9x))y=5cos(9x)	y^{\prime\:}+9(\tan(9x))y=5\cos(9x)
integral of x^5e^{x^{6+1}}	\int\:x^{5}e^{x^{6+1}}dx
(d^2)/(dx^2)((e^x+x^pi)(x^2+x+1))	\frac{d^{2}}{dx^{2}}((e^{x}+x^{π})(x^{2}+x+1))
area y=sqrt(x),y=-x+2,[0,2]	area\:y=\sqrt{x},y=-x+2,[0,2]
area x+y=13,x+7=y^2	area\:x+y=13,x+7=y^{2}
derivative of f(x)=(x^2+4x)/5	derivative\:f(x)=\frac{x^{2}+4x}{5}
limit as x approaches 0-of (11x)/(\|x\|)	\lim\:_{x\to\:0-}(\frac{11x}{\left\|x\right\|})
derivative of 100-ln(2x+1)	\frac{d}{dx}(100-\ln(2x+1))
limit as x approaches 0 of+(sqrt(1/x))	\lim\:_{x\to\:0}(+(\sqrt{\frac{1}{x}}))
integral from-1 to 1 of 1/(x^{4/5)}	\int\:_{-1}^{1}\frac{1}{x^{\frac{4}{5}}}dx
derivative of f(x)=((-7)/(sqrt(7x^2+1)))	derivative\:f(x)=(\frac{-7}{\sqrt{7x^{2}+1}})
limit as x approaches 2 of (2+x)/(x-2)	\lim\:_{x\to\:2}(\frac{2+x}{x-2})
area x-2x^2,-5x	area\:x-2x^{2},-5x
y^'=ty^3-y	y^{\prime\:}=ty^{3}-y
limit as x approaches-2 of (3x^2)-6x+2	\lim\:_{x\to\:-2}((3x^{2})-6x+2)
integral from-2 to 2 of sqrt(1+4x^2)	\int\:_{-2}^{2}\sqrt{1+4x^{2}}dx
area y=sqrt(x),y= 1/3 x	area\:y=\sqrt{x},y=\frac{1}{3}x
sum from n=4 to infinity}(\sqrt{n of)/(n-3)	\sum\:_{n=4}^{\infty\:}\frac{\sqrt{n}}{n-3}
(dy)/(dx)-e^{2x+y}=0	\frac{dy}{dx}-e^{2x+y}=0
derivative of ax^3+bx^2+cx	\frac{d}{dx}(ax^{3}+bx^{2}+cx)
(\partial ^2)/(\partial x\partial y)(x^2-e^{y^2})	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(x^{2}-e^{y^{2}})
integral from 0 to y^3 of xe^{(-x)/y}	\int\:_{0}^{y^{3}}xe^{\frac{-x}{y}}dx
integral of-2-2/x	\int\:-2-\frac{2}{x}dx
(dy}{dx}=\frac{2x^2)/y	\frac{dy}{dx}=\frac{2x^{2}}{y}
derivative of 2x^{2/3}	\frac{d}{dx}(2x^{\frac{2}{3}})
derivative of sqrt(2+3x)	derivative\:\sqrt{2+3x}
derivative of-9sin(3x)	\frac{d}{dx}(-9\sin(3x))
derivative of 9x^9e^{x-1}	\frac{d}{dx}(9x^{9}e^{x-1})
integral of 5/(xln(3x))	\int\:\frac{5}{x\ln(3x)}dx
limit as x approaches 6-of 7-x	\lim\:_{x\to\:6-}(7-x)
integral of 1/(x^{-3)}	\int\:\frac{1}{x^{-3}}dx
y^'=(x+y)/x	y^{\prime\:}=\frac{x+y}{x}
derivative of x+a	\frac{d}{dx}(x+a)
tangent of f(x)=2x^2,\at x=-2	tangent\:f(x)=2x^{2},\at\:x=-2
(\partial)/(\partial y)(ln(x+y)-ln(x-y))	\frac{\partial\:}{\partial\:y}(\ln(x+y)-\ln(x-y))
tangent of y=sqrt(4x+48),(4,8)	tangent\:y=\sqrt{4x+48},(4,8)
inverse oflaplace (74)/(s^2+1)	inverselaplace\:\frac{74}{s^{2}+1}
integral of 3cos^3(3x)	\int\:3\cos^{3}(3x)dx
integral from 4 to 5 of xsqrt(x-4)	\int\:_{4}^{5}x\sqrt{x-4}dx
derivative of-0.5x^2+56x+20	\frac{d}{dx}(-0.5x^{2}+56x+20)
derivative of ((4-y))/((2^y+3))	derivative\:\frac{(4-y)}{(2^{y}+3)}
integral of (-3x+2)e^{-x}	\int\:(-3\cdot\:x+2)\cdot\:e^{-x}dx
derivative of (x/7+7/x ^7)	\frac{d}{dx}((\frac{x}{7}+\frac{7}{x})^{7})

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