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Popular Calculus Problems

integral of (2x)/(x^2-3x-10)	\int\:\frac{2x}{x^{2}-3x-10}dx
(\partial)/(\partial y)(x^{1/2}*y^{1/2})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{2}}\cdot\:y^{\frac{1}{2}})
d/(dt)((cos(t))/(sin(t)))	\frac{d}{dt}(\frac{\cos(t)}{\sin(t)})
derivative of xarctan(2x)	\frac{d}{dx}(x\arctan(2x))
limit as x approaches 0-of xcsc(x)	\lim\:_{x\to\:0-}(x\csc(x))
(d^2)/(dx^2)(cos(-2x))	\frac{d^{2}}{dx^{2}}(\cos(-2x))
derivative of cos(x^2+pi)	\frac{d}{dx}(\cos(x^{2}+π))
derivative of g(t)=sqrt(2)^t	derivative\:g(t)=\sqrt{2}^{t}
taylor x^2e^{x-1},\at 1	taylor\:x^{2}e^{x-1},\at\:1
integral of cot(19x)	\int\:\cot(19x)dx
integral of x^2(3x^3-2)^4	\int\:x^{2}(3x^{3}-2)^{4}dx
derivative of k^x+x^k	\frac{d}{dx}(k^{x}+x^{k})
integral from 0 to 2 of 2pi(x+1)(12-6x)	\int\:_{0}^{2}2π(x+1)(12-6x)dx
derivative of g(x)=3^{(x/2)}	derivative\:g(x)=3^{(\frac{x}{2})}
limit as x approaches 2 of ((3))/(x-2)	\lim\:_{x\to\:2}(\frac{(3)}{x-2})
integral of sec^7(3x)tan(3x)	\int\:\sec^{7}(3x)\tan(3x)dx
limit as x approaches 0-of cot(x)	\lim\:_{x\to\:0-}(\cot(x))
(x(csc(y/x))-y)dx+xdy=0	(x(\csc(\frac{y}{x}))-y)dx+xdy=0
derivative of f(x)=(2x)^3	derivative\:f(x)=(2x)^{3}
tangent of y= 1/((x-1))	tangent\:y=\frac{1}{(x-1)}
(\partial)/(\partial x)(1/(x^2)+y)	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}}+y)
(\partial)/(\partial y)(y^2)	\frac{\partial\:}{\partial\:y}(y^{2})
y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=4	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2t,y(0)=0,y^{\prime\:}(0)=4
(\partial)/(\partial x)(sin(x)cosh(y))	\frac{\partial\:}{\partial\:x}(\sin(x)\cosh(y))
(dy)/(dx)=1+x+y+x*y	\frac{dy}{dx}=1+x+y+x\cdot\:y
limit as x approaches infinity of (1+5/x)^{x/7}	\lim\:_{x\to\:\infty\:}((1+\frac{5}{x})^{\frac{x}{7}})
integral of (2000)/(5x+10)	\int\:\frac{2000}{5x+10}dx
inverse oflaplace ((s+2))/((s^2+s+1))	inverselaplace\:\frac{(s+2)}{(s^{2}+s+1)}
inverse oflaplace (-25)/(s^2+6s+25)	inverselaplace\:\frac{-25}{s^{2}+6s+25}
tangent of f(x)=x^2-8,\at x=4	tangent\:f(x)=x^{2}-8,\at\:x=4
xy^'=3y-6x^2	xy^{\prime\:}=3y-6x^{2}
integral of cos(pix)cos(4pix)	\int\:\cos(πx)\cos(4πx)dx
area 3x,3, 3/x	area\:3x,3,\frac{3}{x}
integral of x/(2ln(x))	\int\:\frac{x}{2\ln(x)}dx
limit as x approaches 1 of x+2	\lim\:_{x\to\:1}(x+2)
limit as x approaches pi of ln(cos(x)-7)	\lim\:_{x\to\:π}(\ln(\cos(x)-7))
f(x)= 1/(3x^{2/3)}	f(x)=\frac{1}{3x^{\frac{2}{3}}}
integral of x^5sqrt(1+x^2)	\int\:x^{5}\sqrt{1+x^{2}}dx
y^{''}=ky	y^{\prime\:\prime\:}=ky
integral of (x^3)/(sqrt(x^2+16))	\int\:\frac{x^{3}}{\sqrt{x^{2}+16}}dx
derivative of \sqrt[4]{x^3}	derivative\:\sqrt[4]{x^{3}}
sum from n=1 to infinity of ((x^n))/(n!)	\sum\:_{n=1}^{\infty\:}\frac{(x^{n})}{n!}
derivative of sin^2(1-s^2)	derivative\:\sin^{2}(1-s^{2})
integral of tan^2(θ)sec^4(θ)	\int\:\tan^{2}(θ)\sec^{4}(θ)dθ
area x^3-3x,x	area\:x^{3}-3x,x
derivative of ln\|4x-3\|	\frac{d}{dx}(\ln\left\|4x-3\right\|)
integral of x(sqrt(2x-1))	\int\:x(\sqrt{2x-1})dx
limit as x approaches pi of ln\|cos(x)-8\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-8\right\|)
integral of e^{-kx}	\int\:e^{-kx}dx
d/(dt)(e^t)	\frac{d}{dt}(e^{t})
limit as x approaches infinity of 3x-5	\lim\:_{x\to\:\infty\:}(3x-5)
integral of x^2*sec^2(x^3)	\int\:x^{2}\cdot\:\sec^{2}(x^{3})dx
limit as x approaches 0 of (x^3-0)/x	\lim\:_{x\to\:0}(\frac{x^{3}-0}{x})
limit as x approaches pi/2 of (1-tan(2x))/(2tan(x))	\lim\:_{x\to\:\frac{π}{2}}(\frac{1-\tan(2x)}{2\tan(x)})
derivative of x^{-8cos(x)}	derivative\:x^{-8\cos(x)}
derivative of 4x^2cos(2x)	\frac{d}{dx}(4x^{2}\cos(2x))
(dy)/(dx)=x+y-1	\frac{dy}{dx}=x+y-1
inverse oflaplace 1/(s^3(s+4))	inverselaplace\:\frac{1}{s^{3}(s+4)}
derivative of 10x^{10}e^x	\frac{d}{dx}(10x^{10}e^{x})
integral of 1/(sqrt(-t^2+8t-15))	\int\:\frac{1}{\sqrt{-t^{2}+8t-15}}dt
derivative of x+e^x-1/x	derivative\:x+e^{x}-\frac{1}{x}
integral of ((4x-5))/((x-2)(x+3))	\int\:\frac{(4x-5)}{(x-2)(x+3)}dx
integral of y/(x(x+y))	\int\:\frac{y}{x(x+y)}dx
xy^'+y=e^x,y(1)=6	xy^{\prime\:}+y=e^{x},y(1)=6
integral of 9/(6+9x)	\int\:\frac{9}{6+9x}dx
integral of (2^x+e^pi)	\int\:(2^{x}+e^{π})dx
derivative of e^7	derivative\:e^{7}
dx+e^3xdy=0	dx+e^{3}xdy=0
tangent of f(x)=x^2,(-1,-3)	tangent\:f(x)=x^{2},(-1,-3)
area x^2-4x,x	area\:x^{2}-4x,x
limit as x approaches 3 of 5(x-3)ln(x-3)	\lim\:_{x\to\:3}(5(x-3)\ln(x-3))
tangent of f(x)= 1/x+3,\at x=-1	tangent\:f(x)=\frac{1}{x}+3,\at\:x=-1
limit as x approaches 5 of-9/(x+5)	\lim\:_{x\to\:5}(-\frac{9}{x+5})
integral from 1 to 3 of 1/(sqrt(3-x))	\int\:_{1}^{3}\frac{1}{\sqrt{3-x}}dx
derivative of (sin(6x))^4	derivative\:(\sin(6x))^{4}
integral from 1 to e of x^3ln(x)	\int\:_{1}^{e}x^{3}\ln(x)dx
derivative of x/(20)	\frac{d}{dx}(\frac{x}{20})
tangent of y=7e^x+x,(0,7)	tangent\:y=7e^{x}+x,(0,7)
inverse oflaplace 4	inverselaplace\:4
integral from 0 to 6 of x^2-6x	\int\:_{0}^{6}x^{2}-6xdx
area x^2,x+5	area\:x^{2},x+5
y^{''}-6y^'+8y=2cos(3t),y(0)=2,y^'(0)=-4	y^{\prime\:\prime\:}-6y^{\prime\:}+8y=2\cos(3t),y(0)=2,y^{\prime\:}(0)=-4
e^yy^'=e^y+4x	e^{y}y^{\prime\:}=e^{y}+4x
derivative of sec^2(2x)	derivative\:\sec^{2}(2x)
ydx+(x^2+4x)dy=0	ydx+(x^{2}+4x)dy=0
(dy)/(dx)=(e^x+7)^2	\frac{dy}{dx}=(e^{x}+7)^{2}
derivative of y=x^2cos(4/x)	derivative\:y=x^{2}\cos(\frac{4}{x})
normal of f(x)=x^4+2e^x,(0,2)	normal\:f(x)=x^{4}+2e^{x},(0,2)
derivative of (sin(x))^2	derivative\:(\sin(x))^{2}
limit as x approaches 0+of-x+5	\lim\:_{x\to\:0+}(-x+5)
taylor e^{-3x}	taylor\:e^{-3x}
limit as x approaches 9-of (x^9)/(x-9)	\lim\:_{x\to\:9-}(\frac{x^{9}}{x-9})
limit as x approaches 0+of xln(x^6)	\lim\:_{x\to\:0+}(x\ln(x^{6}))
tangent of (6x)/((x+1))	tangent\:\frac{6x}{(x+1)}
integral of (7x^2+x+54)/(x^3+9x)	\int\:\frac{7x^{2}+x+54}{x^{3}+9x}dx
derivative of y=sqrt(x+2)	derivative\:y=\sqrt{x+2}
derivative of 5/(25x^2+1)	\frac{d}{dx}(\frac{5}{25x^{2}+1})
integral of (2t^5)/5-(2t^2)/5-(2t)/5	\int\:\frac{2t^{5}}{5}-\frac{2t^{2}}{5}-\frac{2t}{5}dt
derivative of ln(3^{3x})	\frac{d}{dx}(\ln(3^{3x}))
integral from 0 to 1/2 of 5cos(-1(x))	\int\:_{0}^{\frac{1}{2}}5\cos(-1(x))dx

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