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Popular Calculus Problems

(d^2)/(dx^2)(x/(x^2-9))	\frac{d^{2}}{dx^{2}}(\frac{x}{x^{2}-9})
integral of sec^2(7/3 x+4)	\int\:\sec^{2}(\frac{7}{3}x+4)dx
integral of (2x-e^x)	\int\:(2x-e^{x})dx
limit as x approaches 0 of (sin(10x))/(11x)	\lim\:_{x\to\:0}(\frac{\sin(10x)}{11x})
(\partial)/(\partial y)(3xy+y^2)	\frac{\partial\:}{\partial\:y}(3xy+y^{2})
derivative of y=e^x+x^2	derivative\:y=e^{x}+x^{2}
integral of (5e^x)/(e^{2x)+2e^x+1}	\int\:\frac{5e^{x}}{e^{2x}+2e^{x}+1}dx
slope of (-4,0),(1,-5)	slope\:(-4,0),(1,-5)
derivative of sqrt(x^2+2y^2-4)	\frac{d}{dx}(\sqrt{x^{2}+2y^{2}-4})
(y-x)dx+4xdy=0	(y-x)dx+4xdy=0
integral of 1/(sqrt(2x-1))	\int\:\frac{1}{\sqrt{2x-1}}dx
parity ln\|sin(x)\|	parity\:\ln\left\|\sin(x)\right\|
integral of x^4(2x^5-5)^4	\int\:x^{4}(2x^{5}-5)^{4}dx
derivative of x/(sqrt(x^2-1))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}-1}})
integral of ln(2/x)	\int\:\ln(\frac{2}{x})dx
derivative of ((2x^3+4x^2-2x+3))/((x-3))	derivative\:\frac{(2x^{3}+4x^{2}-2x+3)}{(x-3)}
integral of sqrt(x)+3	\int\:\sqrt{x}+3dx
(\partial)/(\partial x)(e^xy+5xy^2-x^2)	\frac{\partial\:}{\partial\:x}(e^{x}y+5xy^{2}-x^{2})
sum from n=0 to infinity of 3/(n^4)	\sum\:_{n=0}^{\infty\:}\frac{3}{n^{4}}
derivative of xcos(x-sin(x))	\frac{d}{dx}(x\cos(x)-\sin(x))
integral of sin(t)cos(nt)	\int\:\sin(t)\cos(nt)dt
y^{''}-3y^'=e^{3t}	y^{\prime\:\prime\:}-3y^{\prime\:}=e^{3t}
integral of (sin^7(12x))/(cos^4(12x))	\int\:\frac{\sin^{7}(12x)}{\cos^{4}(12x)}dx
tangent of f(x)=ln((7(x+3))/x)	tangent\:f(x)=\ln(\frac{7(x+3)}{x})
integral of x^2e^{-x/3}	\int\:x^{2}e^{-\frac{x}{3}}dx
integral from 1 to 5 of 1/(sqrt(4x+5))	\int\:_{1}^{5}\frac{1}{\sqrt{4x+5}}dx
y^{''}-2y=0	y^{\prime\:\prime\:}-2y=0
limit as x approaches-4 of 5x+1	\lim\:_{x\to\:-4}(5x+1)
derivative of arctan(sqrt(x^2-1))	\frac{d}{dx}(\arctan(\sqrt{x^{2}-1}))
derivative of-(6x)/y	derivative\:-\frac{6x}{y}
limit as t approaches 0 of t/(tan(3t))	\lim\:_{t\to\:0}(\frac{t}{\tan(3t)})
derivative of arcsin(x/6)	\frac{d}{dx}(\arcsin(\frac{x}{6}))
derivative of e^{sqrt(xy)}	\frac{d}{dx}(e^{\sqrt{xy}})
derivative of csc(x-cot(x))	\frac{d}{dx}(\csc(x)-\cot(x))
integral of (18x+4)(9x^2+4x)^5	\int\:(18x+4)(9x^{2}+4x)^{5}dx
(\partial)/(\partial x)(-4y^5sin(4x))	\frac{\partial\:}{\partial\:x}(-4y^{5}\sin(4x))
(\partial)/(\partial x)(7x^5y^7+3x^8y^6)	\frac{\partial\:}{\partial\:x}(7x^{5}y^{7}+3x^{8}y^{6})
tangent of f(x)=4(x-1/x)^4,\at x=2	tangent\:f(x)=4(x-\frac{1}{x})^{4},\at\:x=2
sum from n=1 to infinity of 1/(6n)	\sum\:_{n=1}^{\infty\:}\frac{1}{6n}
tangent of \sqrt[4]{x}-x	tangent\:\sqrt[4]{x}-x
inverse oflaplace 2/((s^2+2)(s^2+1))	inverselaplace\:\frac{2}{(s^{2}+2)(s^{2}+1)}
(\partial)/(\partial z)(xz+yz)	\frac{\partial\:}{\partial\:z}(xz+yz)
derivative of f(x)=(x(x^5+9)^3)	derivative\:f(x)=(x(x^{5}+9)^{3})
integral of ln((2-3x)^4)	\int\:\ln((2-3x)^{4})dx
derivative of \sqrt[3]{x^2}+5sqrt(x^3)	\frac{d}{dx}(\sqrt[3]{x^{2}}+5\sqrt{x^{3}})
area sqrt(6x-x^2),0,6	area\:\sqrt{6x-x^{2}},0,6
0.5y^{''}+10y^'+100y=150,y(0)=0,y^'(0)=0	0.5y^{\prime\:\prime\:}+10y^{\prime\:}+100y=150,y(0)=0,y^{\prime\:}(0)=0
derivative of f(x)=(3x+4)/(3x-4)	derivative\:f(x)=\frac{3x+4}{3x-4}
integral of (sin(2x))^3(cos(2x))^2	\int\:(\sin(2x))^{3}(\cos(2x))^{2}dx
integral of (1+x^2)e^{-x}	\int\:(1+x^{2})e^{-x}dx
sum from n=0 to infinity of n/(3n^3+1)	\sum\:_{n=0}^{\infty\:}\frac{n}{3n^{3}+1}
(dy)/(dx)=((x+y))/(3x+3y-4)	\frac{dy}{dx}=\frac{(x+y)}{3x+3y-4}
(2x+3y)dx+(3x+2y)dy=0	(2x+3y)dx+(3x+2y)dy=0
tangent of sqrt(9-6x)	tangent\:\sqrt{9-6x}
derivative of ln(x+y-ln(x-y))	\frac{d}{dx}(\ln(x+y)-\ln(x-y))
(\partial)/(\partial x)(cos(x)-xcos(y))	\frac{\partial\:}{\partial\:x}(\cos(x)-x\cos(y))
integral of 5t^2+e^{0.39t}+2	\int\:5t^{2}+e^{0.39t}+2dt
integral of t/(a+bt^2)	\int\:\frac{t}{a+bt^{2}}dt
integral of 9e^{-9x}	\int\:9e^{-9x}dx
area sin^2(x),sin^3(x)	area\:\sin^{2}(x),\sin^{3}(x)
derivative of sin(1/x x^3)	\frac{d}{dx}(\sin(\frac{1}{x})x^{3})
tangent of g(x)=ln(x^2),(e,2)	tangent\:g(x)=\ln(x^{2}),(e,2)
integral from 0 to 8 of t+2t^3	\int\:_{0}^{8}t+2t^{3}dt
slope of (8.2)(-10.4)	slope\:(8.2)(-10.4)
integral of (x+2)/(x^2-4x)	\int\:\frac{x+2}{x^{2}-4x}dx
(\partial)/(\partial y)(x^3+y^2-yx^2-xy)	\frac{\partial\:}{\partial\:y}(x^{3}+y^{2}-yx^{2}-xy)
limit as x approaches 1-of (x-1)\|x-1\|	\lim\:_{x\to\:1-}((x-1)\left\|x-1\right\|)
derivative of f(x)=4-6x	derivative\:f(x)=4-6x
integral from 2 to 2 of x^3	\int\:_{2}^{2}x^{3}dx
(dy)/(dt)=(te^t)/(ysqrt(1+y^2))	\frac{dy}{dt}=\frac{te^{t}}{y\sqrt{1+y^{2}}}
derivative of-16ax^2+a+1/3	\frac{d}{dx}(-16ax^{2}+a+\frac{1}{3})
integral of xcos(5)x^2	\int\:x\cos(5)x^{2}dx
derivative of y=2xsin(x)+x^2e^x	derivative\:y=2x\sin(x)+x^{2}e^{x}
derivative of-2x^2-5x+2	\frac{d}{dx}(-2x^{2}-5x+2)
integral of 1/(sqrt(x^2-81))	\int\:\frac{1}{\sqrt{x^{2}-81}}dx
y^'=-(3y)/t-2-t^{-4},y(1)=4	y^{\prime\:}=-\frac{3y}{t}-2-t^{-4},y(1)=4
(\partial)/(\partial y)((x-3)/(y^2+1))	\frac{\partial\:}{\partial\:y}(\frac{x-3}{y^{2}+1})
limit as x approaches-infinity of x-5	\lim\:_{x\to\:-\infty\:}(x-5)
integral from-2 to 2 of 32-8y^2	\int\:_{-2}^{2}32-8y^{2}dy
integral from 6 to 8 of (46)/((x-6)^3)	\int\:_{6}^{8}\frac{46}{(x-6)^{3}}dx
tangent of f(x)=(6x)/(x^2-3),(3,3)	tangent\:f(x)=\frac{6x}{x^{2}-3},(3,3)
(dy)/(dx)=-4y+x^3-x	\frac{dy}{dx}=-4y+x^{3}-x
y^{''}-3y^'-4y=3x^2+2	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=3x^{2}+2
integral of (a+bx^6)/(sqrt(7ax+bx^7))	\int\:\frac{a+bx^{6}}{\sqrt{7ax+bx^{7}}}dx
derivative of 4e^{-5t}-3e^{-t}	derivative\:4e^{-5t}-3e^{-t}
(dy)/(dt)+y=sin(t)	\frac{dy}{dt}+y=\sin(t)
laplacetransform tsin(3t)-2tcos(t)	laplacetransform\:t\sin(3t)-2t\cos(t)
taylor 2sin(x^2)	taylor\:2\sin(x^{2})
integral of 2sec^2(x)tan(x)	\int\:2\sec^{2}(x)\tan(x)dx
laplacetransform t^3e^{-2t}	laplacetransform\:t^{3}e^{-2t}
derivative of x*e^{-1/(x^2})	\frac{d}{dx}(x\cdot\:e^{-\frac{1}{x^{2}}})
(e^{-5x})^'	(e^{-5x})^{\prime\:}
integral of (x+4)/x	\int\:\frac{x+4}{x}dx
derivative of ax^3ln(x/4+bx^2(x-4))	\frac{d}{dx}(ax^{3}\ln(\frac{x}{4})+bx^{2}(x-4))
derivative of (e^x/(4-2x))	\frac{d}{dx}(\frac{e^{x}}{4-2x})
(dy)/(dt)=((y+3))/((1-y))	\frac{dy}{dt}=\frac{(y+3)}{(1-y)}
integral of 2csc(x)cot(x)	\int\:2\csc(x)\cot(x)dx
integral of 11θtan^2(θ)	\int\:11θ\tan^{2}(θ)dθ
(\partial)/(\partial x)(-2/3 x-1/3 y+2)	\frac{\partial\:}{\partial\:x}(-\frac{2}{3}x-\frac{1}{3}y+2)
tangent of x+e^x-1/x	tangent\:x+e^{x}-\frac{1}{x}

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