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Popular Calculus Problems

xy(dy)/(dx)=y^2+xsqrt(4x^2+y^2)	xy\frac{dy}{dx}=y^{2}+x\sqrt{4x^{2}+y^{2}}
(\partial}{\partial x}(\frac{-x)/y)	\frac{\partial\:}{\partial\:x}(\frac{-x}{y})
sum from n=1 to infinity of (2n+1)!	\sum\:_{n=1}^{\infty\:}(2n+1)!
integral of 8/(x^3)	\int\:\frac{8}{x^{3}}dx
integral from 0 to infinity of e^{-sx}	\int\:_{0}^{\infty\:}e^{-sx}dx
slope of (2.4)(16.14)	slope\:(2.4)(16.14)
(\partial)/(\partial x)((2x-y)/(2x+y))	\frac{\partial\:}{\partial\:x}(\frac{2x-y}{2x+y})
limit as x approaches 0 of (9sin(x))/(\sqrt[3]{x)}	\lim\:_{x\to\:0}(\frac{9\sin(x)}{\sqrt[3]{x}})
derivative of 4xcos(x)	\frac{d}{dx}(4x\cos(x))
derivative of 2/3 x^{-1/3}	\frac{d}{dx}(\frac{2}{3}x^{-\frac{1}{3}})
integral of (x/y)	\int\:(\frac{x}{y})dy
integral from 4 to infinity of e^{4x}	\int\:_{4}^{\infty\:}e^{4x}dx
integral of sqrt(5-x^2)	\int\:\sqrt{5-x^{2}}dx
integral of x^3*sqrt(1-x^2)	\int\:x^{3}\cdot\:\sqrt{1-x^{2}}dx
area y=x^2(x-11),[-1,12]	area\:y=x^{2}(x-11),[-1,12]
sum from n=1 to infinity of 1/(2n+7)	\sum\:_{n=1}^{\infty\:}\frac{1}{2n+7}
inverse oflaplace 1/((s^2+4)(s^2+2s+2))	inverselaplace\:\frac{1}{(s^{2}+4)(s^{2}+2s+2)}
laplacetransform 2t*sin(t)	laplacetransform\:2t\cdot\:\sin(t)
ty^'-y=(-t^3)/(y^2)	ty^{\prime\:}-y=\frac{-t^{3}}{y^{2}}
7x((dy)/(dx))=2xe^x-7y+6x^2	7x(\frac{dy}{dx})=2xe^{x}-7y+6x^{2}
limit as x approaches 2 of (4x-3)(x^2+5)	\lim\:_{x\to\:2}((4x-3)(x^{2}+5))
derivative of arcsin(2/(x^2))	derivative\:\arcsin(\frac{2}{x^{2}})
integral from 4 to 9 of 2xsqrt(x)	\int\:_{4}^{9}2x\sqrt{x}dx
integral from 11 to 22 of sqrt(484-x^2)	\int\:_{11}^{22}\sqrt{484-x^{2}}dx
sin(x)dy=ycos(x)dx	\sin(x)dy=y\cos(x)dx
y^{''}-2y^'+10y=0,y(0)=-2,y^'(0)=5	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0,y(0)=-2,y^{\prime\:}(0)=5
derivative of (8-3x^2^3)	\frac{d}{dx}((8-3x^{2})^{3})
y^'=xln(x),y(1)=2	y^{\prime\:}=x\ln(x),y(1)=2
integral of x(2+x^3)^2	\int\:x(2+x^{3})^{2}dx
integral of In^2	\int\:In^{2}dx
integral of (1+cos(x))/(cos^2(x))	\int\:\frac{1+\cos(x)}{\cos^{2}(x)}dx
tangent of f(x)=6x^2-6x,\at x=0	tangent\:f(x)=6x^{2}-6x,\at\:x=0
(dx)/(dt)=(x^2-1)t,x(0)=0	\frac{dx}{dt}=(x^{2}-1)t,x(0)=0
integral of sin^2(x	\int\:\sin^{2}(d)xdx
derivative of 12x^3-12x^2	\frac{d}{dx}(12x^{3}-12x^{2})
integral of 7sin^5(x)cos^3(x)	\int\:7\sin^{5}(x)\cos^{3}(x)dx
(\partial)/(\partial y)(xe^{x^2-y})	\frac{\partial\:}{\partial\:y}(xe^{x^{2}-y})
integral of (3x+1)^7	\int\:(3x+1)^{7}dx
limit as x approaches-6+of (x+7)/(x+6)	\lim\:_{x\to\:-6+}(\frac{x+7}{x+6})
(\partial)/(\partial y)(cos(xy)x)	\frac{\partial\:}{\partial\:y}(\cos(xy)x)
derivative of (x^2-2/3 ^{3/2})	\frac{d}{dx}((x^{2}-\frac{2}{3})^{\frac{3}{2}})
derivative of 7/(ln(x))	derivative\:\frac{7}{\ln(x)}
d/(dy)((x^2-y^2)/(x^2+y^2))	\frac{d}{dy}(\frac{x^{2}-y^{2}}{x^{2}+y^{2}})
integral of (4x^3+3x^2+2x+1)	\int\:(4x^{3}+3x^{2}+2x+1)dx
derivative of 1/(sqrt(t))	derivative\:\frac{1}{\sqrt{t}}
integral from-1 to 2 of (x+2-x^2)	\int\:_{-1}^{2}(x+2-x^{2})dx
derivative of 9/(e^x+e^{-x})	\frac{d}{dx}(\frac{9}{e^{x}+e^{-x}})
derivative of 1+x^2	derivative\:1+x^{2}
integral of (x^2)/(sqrt(1-2x^2))	\int\:\frac{x^{2}}{\sqrt{1-2x^{2}}}dx
(\partial)/(\partial x)(ln(3x^2+4y^2+2))	\frac{\partial\:}{\partial\:x}(\ln(3x^{2}+4y^{2}+2))
sum from n=1 to infinity of x^n	\sum\:_{n=1}^{\infty\:}x^{n}
integral of x^6e^{-x}	\int\:x^{6}e^{-x}dx
(\partial)/(\partial y)(cos(yx^2))	\frac{\partial\:}{\partial\:y}(\cos(yx^{2}))
derivative of-(12)/(x^6)	derivative\:-\frac{12}{x^{6}}
derivative of cos(4x^2)	derivative\:\cos(4x^{2})
integral of ((x+9))/(sqrt(x))	\int\:\frac{(x+9)}{\sqrt{x}}dx
integral of 1/(3-3x)	\int\:\frac{1}{3-3x}dx
xyy^'=1+y^2	xyy^{\prime\:}=1+y^{2}
derivative of f(x)=0.882x^{0.842}	derivative\:f(x)=0.882x^{0.842}
derivative of (4x+1sqrt(1+x)/(x^2-1))	\frac{d}{dx}(\frac{4x+1\sqrt{1+x}}{x^{2}-1})
integral from 0 to 5 of f(t)	\int\:_{0}^{5}f(t)dt
derivative of-pisin(pix)	derivative\:-π\sin(πx)
derivative of (x^4+1sech(2ln(x)))	\frac{d}{dx}((x^{4}+1)\sech(2\ln(x)))
limit as x approaches 6+of f(x)	\lim\:_{x\to\:6+}(f(x))
y^'=(xy^'+y)	y^{\prime\:}=(xy^{\prime\:}+y)
derivative of (7x(2x-20^3)/(4x+9))	\frac{d}{dx}(\frac{7x(2x-20)^{3}}{4x+9})
limit as x approaches 0+of x^{1/2}*ln(x)	\lim\:_{x\to\:0+}(x^{\frac{1}{2}}\cdot\:\ln(x))
y^'=4x+y	y^{\prime\:}=4x+y
limit as x approaches 5 of x(x-2)	\lim\:_{x\to\:5}(x(x-2))
integral of ((sqrt(x)+8)^6)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+8)^{6}}{2\sqrt{x}}dx
derivative of 6-6x	derivative\:6-6x
integral of (sqrt(x^3))	\int\:(\sqrt{x^{3}})dx
derivative of y=ln(x+1)	derivative\:y=\ln(x+1)
derivative of (sin(ln(x))^2)	\frac{d}{dx}((\sin(\ln(x)))^{2})
integral of 6/(35sin(x)-12cos(x))	\int\:\frac{6}{35\sin(x)-12\cos(x)}dx
y^{''}+2y^'+3y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+3y=0,y(0)=1,y^{\prime\:}(0)=0
inverse oflaplace tcos(3t)	inverselaplace\:t\cos(3t)
tangent of x^3+y^3=3xy,(3/2 , 3/2)	tangent\:x^{3}+y^{3}=3xy,(\frac{3}{2},\frac{3}{2})
(\partial)/(\partial x)(5e^{4x})	\frac{\partial\:}{\partial\:x}(5e^{4x})
derivative of (1+8x)/(9-2x)	derivative\:\frac{1+8x}{9-2x}
limit as x approaches 1 of 9sqrt(3x^2+1)	\lim\:_{x\to\:1}(9\sqrt{3x^{2}+1})
y^'=12x	y^{\prime\:}=12x
derivative of 2/(sqrt(x+1))	\frac{d}{dx}(\frac{2}{\sqrt{x+1}})
integral of (2x)/(sqrt(1-x^4))	\int\:\frac{2x}{\sqrt{1-x^{4}}}dx
slope of (-2.9)(-1.7)	slope\:(-2.9)(-1.7)
tangent of f(x)=4sin(x),\at x= pi/4	tangent\:f(x)=4\sin(x),\at\:x=\frac{π}{4}
derivative of 3x^2-2x+2	\frac{d}{dx}(3x^{2}-2x+2)
derivative of sin^{sqrt(x)}(x)	\frac{d}{dx}(\sin^{\sqrt{x}}(x))
tangent of f(x)=5x-9x^2,\at x=1	tangent\:f(x)=5x-9x^{2},\at\:x=1
derivative of-8cos(x)	\frac{d}{dx}(-8\cos(x))
derivative of e^xx+2e^x	derivative\:e^{x}x+2e^{x}
integral of (8+x)/(sqrt(64-x^2))	\int\:\frac{8+x}{\sqrt{64-x^{2}}}dx
derivative of 2x(cos(x^2))	\frac{d}{dx}(2x(\cos(x^{2})))
derivative of x^3-12x+2	\frac{d}{dx}(x^{3}-12x+2)
integral of 4+8cos(θ)+4cos^2(θ)	\int\:4+8\cos(θ)+4\cos^{2}(θ)dθ
x^2+y^'=x^2	x^{2}+y^{\prime\:}=x^{2}
(\partial)/(\partial x)(6xe^y)	\frac{\partial\:}{\partial\:x}(6xe^{y})
integral of (-4(ln(x))^4)/x	\int\:\frac{-4(\ln(x))^{4}}{x}dx
derivative of f(x)=(x^2+9)/(sqrt(x))	derivative\:f(x)=\frac{x^{2}+9}{\sqrt{x}}
integral of 3csc^2(t)-5sec(t)tan(t)	\int\:3\csc^{2}(t)-5\sec(t)\tan(t)dt

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