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Popular Calculus Problems

4y^{''}-8y^'+7y=0	4y^{\prime\:\prime\:}-8y^{\prime\:}+7y=0
y^{''}+64y=sec^2(8x)	y^{\prime\:\prime\:}+64y=\sec^{2}(8x)
integral of cos(4x+1)	\int\:\cos(4x+1)dx
integral of tan^3(1)	\int\:\tan^{3}(1)dx
derivative of a*b^x	\frac{d}{dx}(a\cdot\:b^{x})
integral of t^2	\int\:t^{2}dt
(\partial)/(\partial x)(x^2-xy+3y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-xy+3y^{2})
(\partial)/(\partial x)(2xy+x^2-1)	\frac{\partial\:}{\partial\:x}(2xy+x^{2}-1)
limit as x approaches 3 of-3x-6	\lim\:_{x\to\:3}(-3x-6)
derivative of x(1-cos(x))	\frac{d}{dx}(x(1-\cos(x)))
integral from 0 to 2 of (4x^3-3x^2+2x)	\int\:_{0}^{2}(4x^{3}-3x^{2}+2x)dx
integral of 1/5 e^{(-y)/5}	\int\:\frac{1}{5}e^{\frac{-y}{5}}dy
integral of (ln(y^2))/(3y)	\int\:\frac{\ln(y^{2})}{3y}dy
tangent of y=(10x)/(x^2-6),(4,4)	tangent\:y=\frac{10x}{x^{2}-6},(4,4)
limit as x approaches 1 of (ln(x))/(x-1)	\lim\:_{x\to\:1}(\frac{\ln(x)}{x-1})
integral of-20x	\int\:-20xdx
ty^'+2y+t=0	ty^{\prime\:}+2y+t=0
integral of+cos(θ)cos^5(sin(θ))	\int\:+\cos(θ)\cos^{5}(\sin(θ))dθ
x^'= 1/(x^2),x(1)=1	x^{\prime\:}=\frac{1}{x^{2}},x(1)=1
derivative of y= 1/(sqrt(a^2-x^2))	derivative\:y=\frac{1}{\sqrt{a^{2}-x^{2}}}
(\partial)/(\partial x)(e^{x/(b(x))})	\frac{\partial\:}{\partial\:x}(e^{\frac{x}{b(x)}})
limit as t approaches 0 of 5/(1+t)	\lim\:_{t\to\:0}(\frac{5}{1+t})
y^{''}-3y^'=18t+26sin(2t)	y^{\prime\:\prime\:}-3y^{\prime\:}=18t+26\sin(2t)
y^{''}+16y=32sin(4t)	y^{\prime\:\prime\:}+16y=32\sin(4t)
derivative of 2/3 x+4/(3x^2)	\frac{d}{dx}(\frac{2}{3}x+\frac{4}{3x^{2}})
derivative of {f}(x\circ {g}(x))	\frac{d}{dx}({f}(x)\circ\:{g}(x))
limit as x approaches 1-of (x^3-1)/(x-1)	\lim\:_{x\to\:1-}(\frac{x^{3}-1}{x-1})
(x-7)^4y^'+5(x-7)^3y=x+7	(x-7)^{4}y^{\prime\:}+5(x-7)^{3}y=x+7
integral of 1/(tan(y))	\int\:\frac{1}{\tan(y)}dy
y^{''}-8y^'+16y=t^{-7}e^{4t}	y^{\prime\:\prime\:}-8y^{\prime\:}+16y=t^{-7}e^{4t}
limit as x approaches 1+of x^2	\lim\:_{x\to\:1+}(x^{2})
limit as x approaches 5 of x/(x-5)	\lim\:_{x\to\:5}(\frac{x}{x-5})
integral of 1/(y^{1/3)}	\int\:\frac{1}{y^{\frac{1}{3}}}dy
(x-1)y^'+(2x+1)y=0	(x-1)y^{\prime\:}+(2x+1)y=0
d/(ds)(ln((s-1)/(s^2+2s+5)))	\frac{d}{ds}(\ln(\frac{s-1}{s^{2}+2s+5}))
tangent of f(x)=x^2-x+2,\at x=-1	tangent\:f(x)=x^{2}-x+2,\at\:x=-1
9y^{''}+18y^'+17y=0	9y^{\prime\:\prime\:}+18y^{\prime\:}+17y=0
sum from n=1 to infinity of (2n)/(5n+1)	\sum\:_{n=1}^{\infty\:}\frac{2n}{5n+1}
(\partial)/(\partial y)((12x)/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{12x}{x+y})
(dy)/(dx)=y-2	\frac{dy}{dx}=y-2
derivative of sin(3x+1)	derivative\:\sin(3x+1)
limit as x approaches-7 of-13	\lim\:_{x\to\:-7}(-13)
derivative of s(t)= 1/(t+1)	derivative\:s(t)=\frac{1}{t+1}
derivative of cos(e^{-x^2})	derivative\:\cos(e^{-x^{2}})
xy^'+y=x^2ln(x)	xy^{\prime\:}+y=x^{2}\ln(x)
sum from n=1 to infinity of (0.5)^{-n}	\sum\:_{n=1}^{\infty\:}(0.5)^{-n}
integral of 4xcos(3x)	\int\:4x\cos(3x)dx
(\partial)/(\partial u)(sqrt(u^2+v^2))	\frac{\partial\:}{\partial\:u}(\sqrt{u^{2}+v^{2}})
integral of (6ln(4x))/5	\int\:\frac{6\ln(4x)}{5}dx
tangent of-2sin(x)	tangent\:-2\sin(x)
derivative of f(x)=x^5-3x+4	derivative\:f(x)=x^{5}-3x+4
derivative of (e^x)/(x+1)	derivative\:\frac{e^{x}}{x+1}
limit as x approaches 1 of \|x-1\|	\lim\:_{x\to\:1}(\left\|x-1\right\|)
derivative of (x-2/x)	\frac{d}{dx}(\frac{x-2}{x})
derivative of (3x/(2y))	\frac{d}{dx}(\frac{3x}{2y})
integral of x^3sqrt(1+9x^2)	\int\:x^{3}\sqrt{1+9x^{2}}dx
integral of 1+3x^2	\int\:1+3x^{2}dx
limit as x approaches 0 of (e^x+e^{-x}-2)/(xsin(x))	\lim\:_{x\to\:0}(\frac{e^{x}+e^{-x}-2}{x\sin(x)})
integral of 1/(x^2+8x+65)	\int\:\frac{1}{x^{2}+8x+65}dx
integral of e^{11x}	\int\:e^{11x}dx
integral of (cos(sqrt(x)))	\int\:(\cos(\sqrt{x}))dx
limit as x approaches 1/4 of sin(pi/x)	\lim\:_{x\to\:\frac{1}{4}}(\sin(\frac{π}{x}))
derivative of (7x+1^2)	\frac{d}{dx}((7x+1)^{2})
integral of ln(x+(1+x^2)^{1/2})	\int\:\ln(x+(1+x^{2})^{\frac{1}{2}})dx
integral of xyz^2	\int\:xyz^{2}dx
integral of sec(sqrt(x+1))tan(sqrt(x+1))	\int\:\sec(\sqrt{x+1})\tan(\sqrt{x+1})dx
integral of x^2(x^3+1)^{1/4}	\int\:x^{2}(x^{3}+1)^{\frac{1}{4}}dx
(\partial)/(\partial t)(2cos(t))	\frac{\partial\:}{\partial\:t}(2\cos(t))
f(x)=2arctan(x)	f(x)=2\arctan(x)
d/(dy)(1/y)	\frac{d}{dy}(\frac{1}{y})
integral of-cos^3(x)	\int\:-\cos^{3}(x)dx
derivative of sin(3x^2cos(2x))	\frac{d}{dx}(\sin(3)x^{2}\cos(2x))
integral of t*e^t	\int\:t\cdot\:e^{t}dt
y^{''}-y^'+121y=11sin(11t)	y^{\prime\:\prime\:}-y^{\prime\:}+121y=11\sin(11t)
integral of 1/(xsqrt(x-2))	\int\:\frac{1}{x\sqrt{x-2}}dx
y^{''}+4y^'+4y=e^{2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{2x}
integral of 1/(x+1)	\int\:\frac{1}{x+1}dx
maclaurin xe^{x^2}	maclaurin\:xe^{x^{2}}
integral from 1 to sqrt(x of)sec(t)	\int\:_{1}^{\sqrt{x}}\sec(t)dt
derivative of (10/(27x^{8/3)})	\frac{d}{dx}(\frac{10}{27x^{\frac{8}{3}}})
tangent of f(x)=(1+4x)^9,(0,1)	tangent\:f(x)=(1+4x)^{9},(0,1)
derivative of f(x)=-3(2x-2)=0	derivative\:f(x)=-3(2x-2)=0
derivative of (x^4/4-2x^2)	\frac{d}{dx}(\frac{x^{4}}{4}-2x^{2})
slope of (0.1)(2)	slope\:(0.1)(2)
integral of 9xcos(8x)	\int\:9x\cos(8x)dx
y^{''}+4y^'=0	y^{\prime\:\prime\:}+4y^{\prime\:}=0
(\partial)/(\partial y)(xz^2)	\frac{\partial\:}{\partial\:y}(xz^{2})
(d^3)/(dx^3)(4/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{4}{x^{2}})
integral from-1 to 2 of (y+2-y^2)	\int\:_{-1}^{2}(y+2-y^{2})dy
inverse oflaplace (e^{(-pi)/2})/(s^2+9)	inverselaplace\:\frac{e^{\frac{-π}{2}}}{s^{2}+9}
(\partial)/(\partial x)(x^3+x^2y-4y^3)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y-4y^{3})
derivative of \sqrt[5]{sqrt(5x^{3/2)}}	\frac{d}{dx}(\sqrt[5]{\sqrt{5x^{\frac{3}{2}}}})
x((dy)/(dx))+y=3xy^2	x(\frac{dy}{dx})+y=3xy^{2}
integral of 7tan^3(x)sec(x)	\int\:7\tan^{3}(x)\sec(x)dx
(\partial)/(\partial y)(1+x^3+y^4)	\frac{\partial\:}{\partial\:y}(1+x^{3}+y^{4})
(dx)/(dt)=0.25-1/20 x,x(0)=0.5	\frac{dx}{dt}=0.25-\frac{1}{20}x,x(0)=0.5
y^{''}+25y=3sec^3(5)	y^{\prime\:\prime\:}+25y=3\sec^{3}(5)
simplify x/(x^2+y^2)	simplify\:\frac{x}{x^{2}+y^{2}}
sum from n=1 to infinity of 1/(2^nn^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}n^{2}}
derivative of 2x^{-3}	\frac{d}{dx}(2x^{-3})

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