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Popular Calculus Problems

derivative of tan^2(3-2x)	\frac{d}{dx}(\tan^{2}(3-2x))
area sqrt(x),6-x,[4,9]	area\:\sqrt{x},6-x,[4,9]
integral of (2x-3)/(x^2+2x+2)	\int\:\frac{2x-3}{x^{2}+2x+2}dx
limit as x approaches-6 of (x^2-7)/(6-x)	\lim\:_{x\to\:-6}(\frac{x^{2}-7}{6-x})
integral from 0 to 0.5 of 12x-1/12 x	\int\:_{0}^{0.5}12x-\frac{1}{12}xdx
(\partial)/(\partial x)(800-0.001x^2-xy)	\frac{\partial\:}{\partial\:x}(800-0.001x^{2}-xy)
derivative of x*3^x	derivative\:x\cdot\:3^{x}
inverse oflaplace (3s)/(s^2-2s+2)	inverselaplace\:\frac{3s}{s^{2}-2s+2}
integral of x/((4+xy)^2)	\int\:\frac{x}{(4+xy)^{2}}dy
integral of cos^5(9-11x)	\int\:\cos^{5}(9-11x)dx
derivative of (3x-4/(2x-8))	\frac{d}{dx}(\frac{3x-4}{2x-8})
integral of 8x-5	\int\:8x-5dx
area 1/(3(1+x^2)), 1/6 x^2	area\:\frac{1}{3(1+x^{2})},\frac{1}{6}x^{2}
xy^{''}+2y^'=4x^2	xy^{\prime\:\prime\:}+2y^{\prime\:}=4x^{2}
derivative of log_{4}(x^2+3)	\frac{d}{dx}(\log_{4}(x^{2}+3))
integral of 1/(sqrt(x)(\sqrt{x)+1)}	\int\:\frac{1}{\sqrt{x}(\sqrt{x}+1)}dx
tangent of x^3-3x^2+2x-2,\at x=2	tangent\:x^{3}-3x^{2}+2x-2,\at\:x=2
derivative of 2-e^x	\frac{d}{dx}(2-e^{x})
(dy)/(dx)-2/x y=x	\frac{dy}{dx}-\frac{2}{x}y=x
integral of (e^{3.1})^2	\int\:(e^{3.1})^{2}dx
derivative of cos(2sin(x))	\frac{d}{dx}(\cos(2\sin(x)))
limit as x approaches 2 of x^2+2x-1	\lim\:_{x\to\:2}(x^{2}+2x-1)
derivative of sin(pi/4 e^{2x})	\frac{d}{dx}(\sin(\frac{π}{4}e^{2x}))
derivative of 3x^2(x^3+1^7)	\frac{d}{dx}(3x^{2}(x^{3}+1)^{7})
t^2y^{''}-3ty^'+4y=t^2*ln(t)	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}+4y=t^{2}\cdot\:\ln(t)
limit as x approaches 0 of x^6ln(x)	\lim\:_{x\to\:0}(x^{6}\ln(x))
(\partial)/(\partial x)(I/(sqrt(x*y)))	\frac{\partial\:}{\partial\:x}(\frac{I}{\sqrt{x\cdot\:y}})
5y^{''}+y^'=-10x	5y^{\prime\:\prime\:}+y^{\prime\:}=-10x
tangent of (4x)/(x+2)	tangent\:\frac{4x}{x+2}
integral of xe^{x-2}	\int\:xe^{x-2}dx
integral of 1/((4+x^2))	\int\:\frac{1}{(4+x^{2})}dx
limit as x approaches 0 of (3x)/(2x^2-x)	\lim\:_{x\to\:0}(\frac{3x}{2x^{2}-x})
derivative of ((x+4)(x^2-4x+16))/(x^3)	derivative\:\frac{(x+4)(x^{2}-4x+16)}{x^{3}}
integral of 1/3 e^{2-x}	\int\:\frac{1}{3}e^{2-x}dx
derivative of xsqrt(36-x^2)	\frac{d}{dx}(x\sqrt{36-x^{2}})
derivative of (2x+3(5x^2-4x))	\frac{d}{dx}((2x+3)(5x^{2}-4x))
integral from 0 to b of e^{x/2}	\int\:_{0}^{b}e^{\frac{x}{2}}dx
integral of (x^3)/(3x)	\int\:\frac{x^{3}}{3x}dx
limit as x approaches 2 of (f(x))/(g(x))	\lim\:_{x\to\:2}(\frac{f(x)}{g(x)})
integral of ((x^2-x+6))/((x^3-3x))	\int\:\frac{(x^{2}-x+6)}{(x^{3}-3x)}dx
tangent of x^2-6	tangent\:x^{2}-6
(2+x)((dy)/(dx))=3y	(2+x)(\frac{dy}{dx})=3y
derivative of f(x)=(3x)/x ,x=8	derivative\:f(x)=\frac{3x}{x},x=8
tangent of 3x^3-3x	tangent\:3x^{3}-3x
(\partial)/(\partial y)((4ln(y+2))/(xe^x))	\frac{\partial\:}{\partial\:y}(\frac{4\ln(y+2)}{xe^{x}})
integral of 7x	\int\:7xdx
derivative of 4/((x^2-1)^4)	derivative\:\frac{4}{(x^{2}-1)^{4}}
derivative of 6/(5x+2),\at a=-1	derivative\:\frac{6}{5x+2},\at\:a=-1
y^'+6y=60,y(1)=90	y^{\prime\:}+6y=60,y(1)=90
derivative of f(x)=tan(x^2+3x-4)	derivative\:f(x)=\tan(x^{2}+3x-4)
integral of (cos(u))/u	\int\:\frac{\cos(u)}{u}du
(\partial)/(\partial y)((x-y)^{10})	\frac{\partial\:}{\partial\:y}((x-y)^{10})
integral of 1/(sqrt(25x^2-64))	\int\:\frac{1}{\sqrt{25x^{2}-64}}dx
tangent of f(x)=x^7	tangent\:f(x)=x^{7}
derivative of 2tsin(t)	derivative\:2t\sin(t)
derivative of (3x^2+2y^2/((x-2y)^2))	\frac{d}{dx}(\frac{3x^{2}+2y^{2}}{(x-2y)^{2}})
tangent of f(x)=sqrt(x),\at x= 1/9	tangent\:f(x)=\sqrt{x},\at\:x=\frac{1}{9}
derivative of sin(sqrt(2x))	\frac{d}{dx}(\sin(\sqrt{2x}))
(\partial)/(\partial x)(5x^{4/5}y^{1/5})	\frac{\partial\:}{\partial\:x}(5x^{\frac{4}{5}}y^{\frac{1}{5}})
derivative of cos((pix^7))	\frac{d}{dx}(\cos((πx)^{7}))
integral of (6x)/(e^{x^2)}	\int\:\frac{6x}{e^{x^{2}}}dx
derivative of (x^3-3x^4)	\frac{d}{dx}((x^{3}-3x)^{4})
integral of ysin(z)	\int\:y\sin(z)dx
integral of ln(15x)	\int\:\ln(15x)dx
y^{''}-20y^'+100y=0	y^{\prime\:\prime\:}-20y^{\prime\:}+100y=0
(\partial)/(\partial x)(y^{2x})	\frac{\partial\:}{\partial\:x}(y^{2x})
dy-(y-1)^2dx=0	dy-(y-1)^{2}dx=0
limit as x approaches 1 of 2x^3-5x^2+x+6	\lim\:_{x\to\:1}(2x^{3}-5x^{2}+x+6)
integral of cot^3(x)csc^3(x)	\int\:\cot^{3}(x)\csc^{3}(x)dx
derivative of (x^3-4x^2-6x+1(x^2-3x+1))	\frac{d}{dx}((x^{3}-4x^{2}-6x+1)(x^{2}-3x+1))
derivative of x(2x+3^5)	\frac{d}{dx}(x(2x+3)^{5})
laplacetransform 13e^{4t}e^2	laplacetransform\:13e^{4t}e^{2}
derivative of (x-3/(x+4))	\frac{d}{dx}(\frac{x-3}{x+4})
integral from 1 to e of ln(3x)	\int\:_{1}^{e}\ln(3x)dx
derivative of tan^3(x+tan(x^3))	\frac{d}{dx}(\tan^{3}(x)+\tan(x^{3}))
(\partial)/(\partial x)(-2xe^{-xy})	\frac{\partial\:}{\partial\:x}(-2xe^{-xy})
(dy)/(dx)-2xy=x	\frac{dy}{dx}-2xy=x
(dy)/(dx)+y-cos(x)=0	\frac{dy}{dx}+y-\cos(x)=0
derivative of f(x)=x^3(x-1)^2	derivative\:f(x)=x^{3}(x-1)^{2}
derivative of-10ln(xe^{x^8})	derivative\:-10\ln(xe^{x^{8}})
sum from n=1 to infinity of in(1/n)	\sum\:_{n=1}^{\infty\:}in(\frac{1}{n})
derivative of (3x-2/(2x+3))	\frac{d}{dx}(\frac{3x-2}{2x+3})
derivative of g(t)=t^7cos(t)	derivative\:g(t)=t^{7}\cos(t)
derivative of f(x)=(2x-3)^4	derivative\:f(x)=(2x-3)^{4}
integral of 6y(x-y)	\int\:6y(x-y)dy
limit as x approaches 0 of (sqrt(2x+4-2))/(sqrt(x+1-1))	\lim\:_{x\to\:0}(\frac{\sqrt{2x+4-2}}{\sqrt{x+1-1}})
(\partial)/(\partial x)(xyzsqrt(x))	\frac{\partial\:}{\partial\:x}(xyz\sqrt{x})
derivative of e^{-x}-y	\frac{d}{dx}(e^{-x}-y)
integral of 4z^3	\int\:4z^{3}dz
(d^2)/(dx^2)(e^{-2x^2})	\frac{d^{2}}{dx^{2}}(e^{-2x^{2}})
derivative of-1/(cos(x))	\frac{d}{dx}(-\frac{1}{\cos(x)})
sum from n=0 to infinity of cos(pi/2)	\sum\:_{n=0}^{\infty\:}\cos(\frac{π}{2})
tangent of f(x)=4x^2-5x,(-1,9)	tangent\:f(x)=4x^{2}-5x,(-1,9)
sum from n=1 to infinity of (3^n)/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{n^{3}}
integral from 0 to 1 of 7xsqrt(x^2+9)	\int\:_{0}^{1}7x\sqrt{x^{2}+9}dx
integral of (x^2+1)/((x-7)(x-6))	\int\:\frac{x^{2}+1}{(x-7)(x-6)}dx
sum from n=1 to infinity of x^{2n}	\sum\:_{n=1}^{\infty\:}x^{2n}
limit as h approaches 0 of ((2.8^h-1))/h	\lim\:_{h\to\:0}(\frac{(2.8^{h}-1)}{h})
integral of (e^{2t})/(1+e^{4t)}	\int\:\frac{e^{2t}}{1+e^{4t}}dt
integral of (x+2)sin(x^2+4x-6)	\int\:(x+2)\sin(x^{2}+4x-6)dx

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