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Popular Calculus Problems

laplacetransform e^{-1}sin(t)	laplacetransform\:e^{-1}\sin(t)
area x=sqrt(y),x=20-y	area\:x=\sqrt{y},x=20-y
integral of 1/(xsqrt((4x)^2-9))	\int\:\frac{1}{x\sqrt{(4x)^{2}-9}}dx
(\partial)/(\partial x)(-1/(10+2xy))	\frac{\partial\:}{\partial\:x}(-\frac{1}{10+2xy})
integral of sin((npi)/2 x)	\int\:\sin(\frac{nπ}{2}x)dx
derivative of ln(2x^2+1)	derivative\:\ln(2x^{2}+1)
derivative of 3/(x-8)	\frac{d}{dx}(\frac{3}{x-8})
integral of 1/(sin^2(5x))	\int\:\frac{1}{\sin^{2}(5x)}dx
d/(d{z)}({x}{y}{z})	\frac{d}{d{z}}({x}{y}{z})
derivative of ((2x+1))/(x^2)	derivative\:\frac{(2x+1)}{x^{2}}
integral of (x^2-2)/(x^2)	\int\:\frac{x^{2}-2}{x^{2}}dx
limit as x approaches 1 of ln(x)	\lim\:_{x\to\:1}(\ln(x))
integral of (csc^2(x)+1)	\int\:(\csc^{2}(x)+1)dx
(\partial)/(\partial x)(x^2+y)	\frac{\partial\:}{\partial\:x}(x^{2}+y)
(dy)/(dx)+y= 1/(1+x^2)	\frac{dy}{dx}+y=\frac{1}{1+x^{2}}
(dt)/(dt)	\frac{dt}{dt}
integral of arctan(5x-1)	\int\:\arctan(5x-1)dx
derivative of cos(arcsin(x+5))	derivative\:\cos(\arcsin(x+5))
integral of x/(sqrt(9x^2-1))	\int\:\frac{x}{\sqrt{9x^{2}-1}}dx
integral of 1/(sqrt(x^2+8x+19))	\int\:\frac{1}{\sqrt{x^{2}+8x+19}}dx
(\partial)/(\partial x)(ln(ysqrt(x)))	\frac{\partial\:}{\partial\:x}(\ln(y\sqrt{x}))
integral of sin(r^2)r	\int\:\sin(r^{2})rdr
integral of (6^x-4*15^x)/(3^{2x)}	\int\:\frac{6^{x}-4\cdot\:15^{x}}{3^{2x}}dx
derivative of ln(ln(6s))	derivative\:\ln(\ln(6s))
(dy)/(dx)=3e^{x-y}	\frac{dy}{dx}=3e^{x-y}
integral of (kx)/2-x^2	\int\:\frac{kx}{2}-x^{2}dx
limit as x approaches infinity of 0.5x^2	\lim\:_{x\to\:\infty\:}(0.5x^{2})
(\partial)/(\partial x)(-2cos(2x))	\frac{\partial\:}{\partial\:x}(-2\cos(2x))
limit as x approaches 0 of sqrt(4x+48)	\lim\:_{x\to\:0}(\sqrt{4x+48})
laplacetransform-5(t-4)	laplacetransform\:-5(t-4)
derivative of 4x^{2pi}	\frac{d}{dx}(4x^{2π})
tangent of 3x^2-2x+5	tangent\:3x^{2}-2x+5
(dy)/(dx)=8sqrt(x)y	\frac{dy}{dx}=8\sqrt{x}y
limit as x approaches 0 of (arcsin(3x))/(arctan(5x))	\lim\:_{x\to\:0}(\frac{\arcsin(3x)}{\arctan(5x)})
derivative of (x^6/6+6/(x^6))	\frac{d}{dx}(\frac{x^{6}}{6}+\frac{6}{x^{6}})
derivative of sqrt(xe^x)	\frac{d}{dx}(\sqrt{xe^{x}})
derivative of cos(4x-sin(x))	\frac{d}{dx}(\cos(4x)-\sin(x))
integral of (-7x^2)/(sqrt(4x-x^2))	\int\:\frac{-7x^{2}}{\sqrt{4x-x^{2}}}dx
sum from n=1 to infinity of 2/(3n+1)	\sum\:_{n=1}^{\infty\:}\frac{2}{3n+1}
integral of 2xln(4x)	\int\:2x\ln(4x)dx
slope of (6.9)(7.1)	slope\:(6.9)(7.1)
(\partial)/(\partial x)((x-2y)/(x^2-y))	\frac{\partial\:}{\partial\:x}(\frac{x-2y}{x^{2}-y})
derivative of e^{x^2+2}	\frac{d}{dx}(e^{x^{2}+2})
derivative of cos(15x)	\frac{d}{dx}(\cos(15x))
integral of arctan(6x)	\int\:\arctan(6x)dx
y^3-(10x+6)+3xy^2y^'=0	y^{3}-(10x+6)+3xy^{2}y^{\prime\:}=0
integral of (sin^3(x))/(cos^4(x))	\int\:\frac{\sin^{3}(x)}{\cos^{4}(x)}dx
sum from n=1 to infinity of 1/(n(n+6))	\sum\:_{n=1}^{\infty\:}\frac{1}{n(n+6)}
limit as x approaches 0 of (cos(2x))^{1/(x^2)}	\lim\:_{x\to\:0}((\cos(2x))^{\frac{1}{x^{2}}})
integral of 24x^2+2x+10	\int\:24x^{2}+2x+10dx
sum from n=1 to infinity of (-2)^n	\sum\:_{n=1}^{\infty\:}(-2)^{n}
inverse oflaplace ((s+2))/(s^2+7s+12)	inverselaplace\:\frac{(s+2)}{s^{2}+7s+12}
(\partial)/(\partial x)(sin(3x+2y+z))	\frac{\partial\:}{\partial\:x}(\sin(3x+2y+z))
y^{''}-2*y=981,y^'(0)=0,y(0)=0	y^{\prime\:\prime\:}-2\cdot\:y=981,y^{\prime\:}(0)=0,y(0)=0
(\partial}{\partial x}(\frac{(3x+y))/z)	\frac{\partial\:}{\partial\:x}(\frac{(3x+y)}{z})
(\partial)/(\partial x)(sin((x-y)/(x+y)))	\frac{\partial\:}{\partial\:x}(\sin(\frac{x-y}{x+y}))
integral of sin^2(8x)cos^2(8x)	\int\:\sin^{2}(8x)\cos^{2}(8x)dx
(dy)/(dx)=-(xy)/(ln(y))	\frac{dy}{dx}=-\frac{xy}{\ln(y)}
integral of 1/(2xsqrt(4x^2-8))	\int\:\frac{1}{2x\sqrt{4x^{2}-8}}dx
(\partial)/(\partial x)(x^{nxy})	\frac{\partial\:}{\partial\:x}(x^{nxy})
derivative of sqrt(9x^2)	\frac{d}{dx}(\sqrt{9x^{2}})
integral of e^{i6x}cos(3x)	\int\:e^{i6x}\cos(3x)dx
integral of-cos(x)3x^2	\int\:-\cos(x)3x^{2}dx
integral of 1/(3x+6)	\int\:\frac{1}{3x+6}dx
limit as x approaches 1-of 1/(x-1)	\lim\:_{x\to\:1-}(\frac{1}{x-1})
derivative of-5xsqrt(x)	derivative\:-5x\sqrt{x}
integral of-4cos(x/2)+5	\int\:-4\cos(\frac{x}{2})+5dx
(x+1)y^'+(x+2)y=2xe^{-2}	(x+1)y^{\prime\:}+(x+2)y=2xe^{-2}
integral of sqrt(49x^2+1764)	\int\:\sqrt{49x^{2}+1764}dx
integral of (x*e^{2x})/((1+2x)^2)	\int\:\frac{x\cdot\:e^{2x}}{(1+2x)^{2}}dx
(\partial)/(\partial y)(cos(xy^2))	\frac{\partial\:}{\partial\:y}(\cos(xy^{2}))
limit as x approaches-2 of x-1	\lim\:_{x\to\:-2}(x-1)
integral of sin(x)in(x)	\int\:\sin(x)d\sin(x)dx
limit as x approaches 3 of x^3-x^2+15	\lim\:_{x\to\:3}(x^{3}-x^{2}+15)
volumeabout y=0,y=cos(x),[0,(3pi)/2 ]	volumeabout\:y=0,y=\cos(x),[0,\frac{3π}{2}]
limit as x approaches 0 of (-2x)/(x-3)	\lim\:_{x\to\:0}(\frac{-2x}{x-3})
integral of 10x(x^2+3)^4	\int\:10x(x^{2}+3)^{4}dx
derivative of f(x)=\sqrt[3]{x^6+8}	derivative\:f(x)=\sqrt[3]{x^{6}+8}
integral from 0 to 1 of (33)/(x^5)	\int\:_{0}^{1}\frac{33}{x^{5}}dx
integral of e^{-(s-a)t}	\int\:e^{-(s-a)t}dt
derivative of (3+x^5)^{2/3}	derivative\:(3+x^{5})^{\frac{2}{3}}
derivative of pi*x	\frac{d}{dx}(π\cdot\:x)
d/(dt)(cos(t^2))	\frac{d}{dt}(\cos(t^{2}))
derivative of pi/x	\frac{d}{dx}(\frac{π}{x})
derivative of-3x^4-1/x+xsqrt(x)	\frac{d}{dx}(-3x^{4}-\frac{1}{x}+x\sqrt{x})
limit as x approaches-pi/4 of-sec(2x)	\lim\:_{x\to\:-\frac{π}{4}}(-\sec(2x))
derivative of f(x)=(3x^2+4x-19)^{15}	derivative\:f(x)=(3x^{2}+4x-19)^{15}
y^'+ycos(x)=5cos(x)	y^{\prime\:}+y\cos(x)=5\cos(x)
integral of sin^4(y)cos^4(y)	\int\:\sin^{4}(y)\cos^{4}(y)dy
f(x)=sin(pix)	f(x)=\sin(πx)
limit as x approaches 5 of sqrt(5-x^2)	\lim\:_{x\to\:5}(\sqrt{5-x^{2}})
derivative of (2x^2-4/((x+4)^2))	\frac{d}{dx}(\frac{2x^{2}-4}{(x+4)^{2}})
y^{'''}-y^{''}-y^'+y=2e^{-x}+3	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}-y^{\prime\:}+y=2e^{-x}+3
area f(x)= 1/(4(1+x^2)),g(x)= 1/8 x^2	area\:f(x)=\frac{1}{4(1+x^{2})},g(x)=\frac{1}{8}x^{2}
derivative of (2y/(x^2+y^2))	\frac{d}{dx}(\frac{2y}{x^{2}+y^{2}})
limit as x approaches 45 of (x^2)/9-5/x	\lim\:_{x\to\:45}(\frac{x^{2}}{9}-\frac{5}{x})
derivative of sin^5(2x)	\frac{d}{dx}(\sin^{5}(2x))
(\partial)/(\partial x)(xe^{x^2})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}})
xy^'-x^2y=-x^2	xy^{\prime\:}-x^{2}y=-x^{2}
derivative of x^2-3x+2	derivative\:x^{2}-3x+2

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