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Popular Calculus Problems

limit as n approaches infinity of sin(2n)	\lim\:_{n\to\:\infty\:}(\sin(2n))
taylor e^{-3x},0	taylor\:e^{-3x},0
sum from n=2 to infinity of x^n	\sum\:_{n=2}^{\infty\:}x^{n}
(dy}{dx}=-\frac{sin(x))/y	\frac{dy}{dx}=-\frac{\sin(x)}{y}
integral of cos(r^2)	\int\:\cos(r^{2})dr
xy^'=(1-x)y+x^2+x^3	xy^{\prime\:}=(1-x)y+x^{2}+x^{3}
y^{''}+4y^'=cos^2(x)	y^{\prime\:\prime\:}+4y^{\prime\:}=\cos^{2}(x)
integral of-1/(10-x)	\int\:-\frac{1}{10-x}dx
integral of cos^3(x)(sin(x))	\int\:\cos^{3}(x)(\sin(x))dx
area y=x^2-8,y=1	area\:y=x^{2}-8,y=1
derivative of y=5e^{5t+1}	derivative\:y=5e^{5t+1}
derivative of ln(cos(x)+x)	\frac{d}{dx}(\ln(\cos(x))+x)
integral of (x^2)/((9x^2-4)^{5/2)}	\int\:\frac{x^{2}}{(9x^{2}-4)^{\frac{5}{2}}}dx
integral from 0 to pi of (5e^x+3sin(x))	\int\:_{0}^{π}(5e^{x}+3\sin(x))dx
(\partial)/(\partial x)(3tsin^2(t))	\frac{\partial\:}{\partial\:x}(3t\sin^{2}(t))
derivative of f(x)=5x-1	derivative\:f(x)=5x-1
x^4y^'+3x^3y=x^2e^x	x^{4}y^{\prime\:}+3x^{3}y=x^{2}e^{x}
derivative of (3x-9/(2x+4))	\frac{d}{dx}(\frac{3x-9}{2x+4})
integral of 1/(sqrt(16x^2+25))	\int\:\frac{1}{\sqrt{16x^{2}+25}}dx
integral of sqrt(15-2x-x^2)	\int\:\sqrt{15-2x-x^{2}}dx
(dy)/(dt)+k(340-y)=0	\frac{dy}{dt}+k(340-y)=0
laplacetransform e	laplacetransform\:e
integral of-4x^2(4x^3-1)^7	\int\:-4x^{2}(4x^{3}-1)^{7}dx
f(x)=x^{2x}	f(x)=x^{2x}
derivative of a(e^x+e^{xx})	\frac{d}{dx}(a(e^{x}+e^{xx}))
derivative of f(x)= 1/(sqrt(x+1))	derivative\:f(x)=\frac{1}{\sqrt{x+1}}
limit as x approaches infinity of y^{-x}	\lim\:_{x\to\:\infty\:}(y^{-x})
limit as x approaches 2 of 5	\lim\:_{x\to\:2}(5)
area e^{-x},0,0,ln(3)	area\:e^{-x},0,0,\ln(3)
(dy)/(dt)=6y+2t-4,y(0)=3	\frac{dy}{dt}=6y+2t-4,y(0)=3
limit as x approaches 4 of (x^2)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{2}}{x-4})
integral of 12xln(2x)	\int\:12x\ln(2x)dx
derivative of e^{x*y}	\frac{d}{dx}(e^{x\cdot\:y})
parity f(x)=sin(tan(sqrt(1+x^3)))	parity\:f(x)=\sin(\tan(\sqrt{1+x^{3}}))
limit as x approaches 3 of x/2	\lim\:_{x\to\:3}(\frac{x}{2})
derivative of 1/(arcsec(x))	\frac{d}{dx}(\frac{1}{\arcsec(x)})
d/(dt)(cos(wt))	\frac{d}{dt}(\cos(wt))
integral of 2e^xcos(x)	\int\:2e^{x}\cos(x)dx
(\partial)/(\partial y)(e^y)	\frac{\partial\:}{\partial\:y}(e^{y})
(\partial)/(\partial x)(4xy-x^4-y^4+1)	\frac{\partial\:}{\partial\:x}(4xy-x^{4}-y^{4}+1)
integral from 0 to x of e^{-t^2}	\int\:_{0}^{x}e^{-t^{2}}dt
derivative of (x+1)/(4x^2+12x+2)	derivative\:\frac{x+1}{4x^{2}+12x+2}
derivative of 3arcsin(x^2)	\frac{d}{dx}(3\arcsin(x^{2}))
integral from 1 to 2 of 4^x	\int\:_{1}^{2}4^{x}dx
area 4x^2,(sqrt(x))/2	area\:4x^{2},\frac{\sqrt{x}}{2}
limit as x approaches 0-of-x+3	\lim\:_{x\to\:0-}(-x+3)
integral from-1 to 1 of pi(1-x^2)	\int\:_{-1}^{1}π(1-x^{2})dx
limit as x approaches infinity of 1.003	\lim\:_{x\to\:\infty\:}(1.003)
y^'=xy^3(1+x^2)^{-1/2}	y^{\prime\:}=xy^{3}(1+x^{2})^{-\frac{1}{2}}
derivative of f(x)=(x^2+8)(7-x)	derivative\:f(x)=(x^{2}+8)(7-x)
limit as x approaches 1 of e^{1/(x-1)}	\lim\:_{x\to\:1}(e^{\frac{1}{x-1}})
integral of (4x)/(sqrt(3x))	\int\:\frac{4x}{\sqrt{3x}}dx
integral from 1 to 4 of 2/(x^2)	\int\:_{1}^{4}\frac{2}{x^{2}}dx
derivative of sin^6(pix)	\frac{d}{dx}(\sin^{6}(πx))
integral of (x^2+x)/((x-3)(x^2+1))	\int\:\frac{x^{2}+x}{(x-3)(x^{2}+1)}dx
integral of (7x^3)/(sqrt(7+x^2))	\int\:\frac{7x^{3}}{\sqrt{7+x^{2}}}dx
derivative of x^3+x^2+1	\frac{d}{dx}(x^{3}+x^{2}+1)
derivative of x/(sqrt(1+5x^2))	\frac{d}{dx}(\frac{x}{\sqrt{1+5x^{2}}})
(t-1)^2y^'+3(t-1)y=t+2	(t-1)^{2}y^{\prime\:}+3(t-1)y=t+2
limit as x approaches 0 of (1-ln(x))/(e^{1/x)}	\lim\:_{x\to\:0}(\frac{1-\ln(x)}{e^{\frac{1}{x}}})
derivative of \sqrt[5]{x^5-x^3+3}	\frac{d}{dx}(\sqrt[5]{x^{5}-x^{3}+3})
derivative of e^{-2x+x^2}	\frac{d}{dx}(e^{-2x+x^{2}})
integral from 0 to 2 of x-sqrt(x)	\int\:_{0}^{2}x-\sqrt{x}dx
inverse oflaplace s/((s^2+4s+5))	inverselaplace\:\frac{s}{(s^{2}+4s+5)}
area 4-x^2,-2,2	area\:4-x^{2},-2,2
integral of (x-3)cos(x)	\int\:(x-3)\cos(x)dx
limit as x approaches 3+of e^{x/(3-x)}	\lim\:_{x\to\:3+}(e^{\frac{x}{3-x}})
(\partial)/(\partial θ)(-cos(θ))	\frac{\partial\:}{\partial\:θ}(-\cos(θ))
area y=sqrt(x),y= 1/3 x,x=16	area\:y=\sqrt{x},y=\frac{1}{3}x,x=16
limit as x approaches 3 of (x^2+4x-2)^2	\lim\:_{x\to\:3}((x^{2}+4x-2)^{2})
d/(da)((x-a)^2)	\frac{d}{da}((x-a)^{2})
limit as x approaches 2 of x-2	\lim\:_{x\to\:2}(x-2)
tangent of f(x)= x/(1+x^2),\at x=0	tangent\:f(x)=\frac{x}{1+x^{2}},\at\:x=0
derivative of-x^2+6	\frac{d}{dx}(-x^{2}+6)
limit as x approaches 5-of-2/(sqrt(5-x))	\lim\:_{x\to\:5-}(-\frac{2}{\sqrt{5-x}})
(\partial)/(\partial x)(50y+3250-100x)	\frac{\partial\:}{\partial\:x}(50y+3250-100x)
integral of (1+2x^2)e^{-2x}	\int\:(1+2x^{2})e^{-2x}dx
(x^3+y^3)dx+(3xy^2)dy=0	(x^{3}+y^{3})dx+(3xy^{2})dy=0
derivative of y=(x^2-16)/(x^2)	derivative\:y=\frac{x^{2}-16}{x^{2}}
derivative of (x^2/(7+x))	\frac{d}{dx}(\frac{x^{2}}{7+x})
integral of (2x^3-x^2+4x-4)/(x^4-4x^2)	\int\:\frac{2x^{3}-x^{2}+4x-4}{x^{4}-4x^{2}}dx
integral from 0 to 2 of 10^x	\int\:_{0}^{2}10^{x}dx
derivative of e^{3x}-1-3x	\frac{d}{dx}(e^{3x}-1-3x)
derivative of f(x)=(2(-x^2+1))/((x^2+1))	derivative\:f(x)=\frac{2(-x^{2}+1)}{(x^{2}+1)}
tangent of f(x)=2\sqrt[3]{x},\at x=64	tangent\:f(x)=2\sqrt[3]{x},\at\:x=64
derivative of x^5-20x^3+64x	\frac{d}{dx}(x^{5}-20x^{3}+64x)
derivative of (10x^3/(x^2-1))	\frac{d}{dx}(\frac{10x^{3}}{x^{2}-1})
integral of ((sqrt(x^2-16)))/x	\int\:\frac{(\sqrt{x^{2}-16})}{x}dx
derivative of arctan(ln(x))	\frac{d}{dx}(\arctan(\ln(x)))
(\partial)/(\partial x)(x^4y^8+4x^5y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{8}+4x^{5}y)
derivative of ln(x/(x^2+2))	derivative\:\ln(\frac{x}{x^{2}+2})
derivative of 5log_{2}(x)	\frac{d}{dx}(5\log_{2}(x))
y^{''}+10y^'+25y=0,y(0)=0,y(pi/2)=1	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=0,y(0)=0,y(\frac{π}{2})=1
inverse oflaplace 8/((s-1)^3)	inverselaplace\:\frac{8}{(s-1)^{3}}
integral of x^3sqrt(x^2-16)	\int\:x^{3}\sqrt{x^{2}-16}dx
derivative of 5-\|x\|	\frac{d}{dx}(5-\left\|x\right\|)
integral of tan(3xse)c^23x	\int\:\tan(3xse)c^{2}3xdx
limit as x approaches-3 of sqrt(x^2+x)-x	\lim\:_{x\to\:-3}(\sqrt{x^{2}+x}-x)
integral from 0 to 1 of x/(x^3+1)	\int\:_{0}^{1}\frac{x}{x^{3}+1}dx
derivative of (x-6/(x^2-2x+12))	\frac{d}{dx}(\frac{x-6}{x^{2}-2x+12})

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