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Popular Calculus Problems

tangent of y=cot(x),\at x= pi/4	tangent\:y=\cot(x),\at\:x=\frac{π}{4}
derivative of sin(ax^2)	\frac{d}{dx}(\sin(ax^{2}))
integral of sqrt(t^3+1)	\int\:\sqrt{t^{3}+1}dt
integral from 6 to 8 of (88)/((x-6)^3)	\int\:_{6}^{8}\frac{88}{(x-6)^{3}}dx
integral of x(x-1)^7	\int\:x(x-1)^{7}dx
integral of e+sec^2(θ)-e^θ	\int\:e+\sec^{2}(θ)-e^{θ}dθ
derivative of cot^3(4x+1)	derivative\:\cot^{3}(4x+1)
derivative of-x^4+sqrt(x)	\frac{d}{dx}(-x^{4}+\sqrt{x})
(xdy)/(dx)-(1+x)y=xy^2	\frac{xdy}{dx}-(1+x)y=xy^{2}
integral of (3-1/x)^{-2}(1/(x^2))	\int\:(3-\frac{1}{x})^{-2}(\frac{1}{x^{2}})dx
integral of (x^3)/((5-x^4)^5)	\int\:\frac{x^{3}}{(5-x^{4})^{5}}dx
tangent of y=4(x-1/x)^3,\at x=2	tangent\:y=4(x-\frac{1}{x})^{3},\at\:x=2
integral of 1/((x-1)sqrt(4x^2-8x+3))	\int\:\frac{1}{(x-1)\sqrt{4x^{2}-8x+3}}dx
integral of x+2/(sin^2(x))	\int\:x+\frac{2}{\sin^{2}(x)}dx
y^{''}-y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}-y=0,y(0)=0,y^{\prime\:}(0)=1
derivative of 8cos^4(x)	\frac{d}{dx}(8\cos^{4}(x))
limit as x approaches-1 of f(x)	\lim\:_{x\to\:-1}(f(x))
parity 1.1^x+9^xdx	parity\:1.1^{x}+9^{x}dx
derivative of (40)/(x^9)	derivative\:\frac{40}{x^{9}}
limit as x approaches-1 of (x^3)/(x^2+1)	\lim\:_{x\to\:-1}(\frac{x^{3}}{x^{2}+1})
(\partial)/(\partial x)(ue^{2x})	\frac{\partial\:}{\partial\:x}(ue^{2x})
integral of (-8)/((x-2)(x^2+4))	\int\:\frac{-8}{(x-2)(x^{2}+4)}dx
-3y^'+9x^2=0	-3y^{\prime\:}+9x^{2}=0
(\partial)/(\partial x)(6y^2sqrt(x))	\frac{\partial\:}{\partial\:x}(6y^{2}\sqrt{x})
(xsqrt(x))^'	(x\sqrt{x})^{\prime\:}
(dy)/(dt)+7y=e^{4t},y(0)=10	\frac{dy}{dt}+7y=e^{4t},y(0)=10
(\partial)/(\partial x)(e^{-ax^2})	\frac{\partial\:}{\partial\:x}(e^{-ax^{2}})
(x+4)^2y^'+3(x+4)y=4	(x+4)^{2}y^{\prime\:}+3(x+4)y=4
integral of (50)/((x-1)(x^2+49))	\int\:\frac{50}{(x-1)(x^{2}+49)}dx
derivative of ln(e^{x^2})	derivative\:\ln(e^{x^{2}})
integral of (x^2)/(sqrt(x^2-4x+13))	\int\:\frac{x^{2}}{\sqrt{x^{2}-4x+13}}dx
integral of (e^{4x})/2	\int\:\frac{e^{4x}}{2}dx
limit as x approaches 0 of sqrt(x)*ln(x)	\lim\:_{x\to\:0}(\sqrt{x}\cdot\:\ln(x))
limit as x approaches 3 of 4^{f(x)}	\lim\:_{x\to\:3}(4^{f(x)})
integral from 1 to 2x of y/x	\int\:_{1}^{2x}\frac{y}{x}dx
implicit (dy)/(dx),xy=2y+x	implicit\:\frac{dy}{dx},xy=2y+x
derivative of f(x)=-x^3+x^2+4x-2	derivative\:f(x)=-x^{3}+x^{2}+4x-2
derivative of e^{-3x}(2cos(2x-3sin(2x)))	\frac{d}{dx}(e^{-3x}(2\cos(2x)-3\sin(2x)))
integral of (6x)/(\sqrt[4]{x+2)}	\int\:\frac{6x}{\sqrt[4]{x+2}}dx
limit as x approaches 0 of 2/(3-e^{1/x)}	\lim\:_{x\to\:0}(\frac{2}{3-e^{\frac{1}{x}}})
integral of 1/(sqrt(x)(1-\sqrt{x))}	\int\:\frac{1}{\sqrt{x}(1-\sqrt{x})}dx
integral of (x^2-x)e^x	\int\:(x^{2}-x)e^{x}dx
y^'=y(1-y),y(0)=12	y^{\prime\:}=y(1-y),y(0)=12
integral of 1/(x^2sqrt(3x-1))	\int\:\frac{1}{x^{2}\sqrt{3x-1}}dx
integral of 2x(x^2+3)^4	\int\:2x(x^{2}+3)^{4}dx
(\partial)/(\partial y)(ysin(xy))	\frac{\partial\:}{\partial\:y}(y\sin(xy))
derivative of (ln(x)^5)	\frac{d}{dx}((\ln(x))^{5})
integral of 8xe^{8x}	\int\:8xe^{8x}dx
derivative of ln^3(x)	derivative\:\ln^{3}(x)
(dy}{dx}=\frac{(1-3y)^2)/x ,y(1)=1	\frac{dy}{dx}=\frac{(1-3y)^{2}}{x},y(1)=1
derivative of (x^2+1^2)	\frac{d}{dx}((x^{2}+1)^{2})
sum from n=0 to infinity of (n^2)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}}{n!}
derivative of sin(3xln(sech(2x)))	\frac{d}{dx}(\sin(3x)\ln(\sech(2x)))
(\partial)/(\partial y)(ln(x^2+y^2+2))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{2}+2))
sum from n=1 to infinity of (x^n)/(1^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{1^{n}}
integral of (1+x)^3	\int\:(1+x)^{3}dx
derivative of f(x)=(x^2-3x+4)/(x+2)	derivative\:f(x)=\frac{x^{2}-3x+4}{x+2}
area 1+x-x^2-x^3,1-x	area\:1+x-x^{2}-x^{3},1-x
derivative of 6/(2x+1)	\frac{d}{dx}(\frac{6}{2x+1})
derivative of sqrt(((x+1/(x+6))^8))	\frac{d}{dx}(\sqrt{(\frac{x+1}{x+6})^{8}})
y^'= 1/((t-1)(y+1))	y^{\prime\:}=\frac{1}{(t-1)(y+1)}
derivative of f(x)=x^3(x-6)^2	derivative\:f(x)=x^{3}(x-6)^{2}
f(x)=sqrt(x-1)+sqrt(x+1)	f(x)=\sqrt{x-1}+\sqrt{x+1}
tangent of y=(((x+2))/((x-2)))^2,\at x=3	tangent\:y=(\frac{(x+2)}{(x-2)})^{2},\at\:x=3
integral from 0 to pi of 14sin^4(x)	\int\:_{0}^{π}14\sin^{4}(x)dx
integral of (x-1)/((x+1)^3)	\int\:\frac{x-1}{(x+1)^{3}}dx
limit as x approaches 5 of x+3	\lim\:_{x\to\:5}(x+3)
y^'+1=2y	y^{\prime\:}+1=2y
integral of x/((x^2-4)^3)	\int\:\frac{x}{(x^{2}-4)^{3}}dx
derivative of (ax^2/(ln(x/4)))	\frac{d}{dx}(\frac{ax^{2}}{\ln(\frac{x}{4})})
y^'=(x-y)/x	y^{\prime\:}=\frac{x-y}{x}
derivative of e^{-(x+2)}-sin(x^2)+1	derivative\:e^{-(x+2)}-\sin(x^{2})+1
derivative of (x^2)/4+x+1	derivative\:\frac{x^{2}}{4}+x+1
integral of 1/(sin(x)-2csc(x))	\int\:\frac{1}{\sin(x)-2\csc(x)}dx
tangent of y=(5x)/(x-2),(3,15)	tangent\:y=\frac{5x}{x-2},(3,15)
slope of f(x)=(x^2)/(x+4)	slope\:f(x)=\frac{x^{2}}{x+4}
integral of (6e^x)	\int\:(6e^{x})dx
sum from n=0 to infinity of 7/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{7}{2^{n}}
derivative of e^xx^6+12e^xx^5+30e^xx^4	\frac{d}{dx}(e^{x}x^{6}+12e^{x}x^{5}+30e^{x}x^{4})
integral of (2+sqrt(5))	\int\:(2+\sqrt{5})dx
derivative of 1/(sqrt(1-x^2))	derivative\:\frac{1}{\sqrt{1-x^{2}}}
integral of cos(sqrt(t))	\int\:\cos(\sqrt{t})dt
integral from-64 to 64 of 1/(x^{1/3)}	\int\:_{-64}^{64}\frac{1}{x^{\frac{1}{3}}}dx
(\partial)/(\partial y)(x^3+3x^2y-2y^2)	\frac{\partial\:}{\partial\:y}(x^{3}+3x^{2}y-2y^{2})
derivative of \sqrt[3]{1+7x}	derivative\:\sqrt[3]{1+7x}
inverse oflaplace 1/(s(s^2-2s+2))	inverselaplace\:\frac{1}{s(s^{2}-2s+2)}
y^'+y+1/x y=(e^{-x})/x	y^{\prime\:}+y+\frac{1}{x}y=\frac{e^{-x}}{x}
derivative of f(x)=x^{9/2}	derivative\:f(x)=x^{\frac{9}{2}}
3y^{''}-4y^'-15y=0	3y^{\prime\:\prime\:}-4y^{\prime\:}-15y=0
derivative of 2/3 (x^2+1)^{3/2}	derivative\:\frac{2}{3}(x^{2}+1)^{\frac{3}{2}}
(\partial)/(\partial x)(arcsin(5xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(5xyz))
integral of e^{3x}x	\int\:e^{3x}xdx
sum from n=0 to infinity of 1/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+2}
integral of (sqrt(9-x^2))/(3x)	\int\:\frac{\sqrt{9-x^{2}}}{3x}dx
parity sec(sin(x))	parity\:\sec(\sin(x))
(dS)/(dt)=0.9-(15S)/(1000)	\frac{dS}{dt}=0.9-\frac{15S}{1000}
2x^3dy=y(2x^2-y^3)dx	2x^{3}dy=y(2x^{2}-y^{3})dx
integral of cos^3(t)sin(t)	\int\:\cos^{3}(t)\sin(t)dt
integral of (cot(ln(x)))/x	\int\:\frac{\cot(\ln(x))}{x}dx
integral from 0 to 1 of 2x^2sqrt(x^2+4)	\int\:_{0}^{1}2x^{2}\sqrt{x^{2}+4}dx

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