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Popular Calculus Problems

limit as x approaches-6-of (x+2)/(x+6)	\lim\:_{x\to\:-6-}(\frac{x+2}{x+6})
integral of 9/(x^2-9x)	\int\:\frac{9}{x^{2}-9x}dx
taylor x/(1+x^2)	taylor\:\frac{x}{1+x^{2}}
integral of ax^2	\int\:ax^{2}dx
derivative of 5-(x-9)^4	derivative\:5-(x-9)^{4}
derivative of (1/(x^2-7/(x^4))(x+5x^3))	\frac{d}{dx}((\frac{1}{x^{2}}-\frac{7}{x^{4}})(x+5x^{3}))
integral of x^3cos^2(x)	\int\:x^{3}\cos^{2}(x)dx
integral of 1/(sqrt(4^2-x^2))	\int\:\frac{1}{\sqrt{4^{2}-x^{2}}}dx
derivative of t/((t-6)^2)	derivative\:\frac{t}{(t-6)^{2}}
limit as x approaches-8-of (\|x+8\|)/(x+8)	\lim\:_{x\to\:-8-}(\frac{\left\|x+8\right\|}{x+8})
sum from n=0 to infinity of (x^n)/(n+1)	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{n+1}
derivative of f(x)=(3x+1)(5x-4)	derivative\:f(x)=(3x+1)(5x-4)
derivative of (45-0.12xx)	\frac{d}{dx}((45-0.12x)x)
integral of-6x^2+10	\int\:-6x^{2}+10dx
(dr)/(dθ)+rtan(θ)=sec(θ)tan(θ)	\frac{dr}{dθ}+r\tan(θ)=\sec(θ)\tan(θ)
y^'-4y=x	y^{\prime\:}-4y=x
derivative of f(x)=x^2+3x^6	derivative\:f(x)=x^{2}+3x^{6}
(\partial)/(\partial x)(e^{2y})	\frac{\partial\:}{\partial\:x}(e^{2y})
(\partial)/(\partial y)(x^2y+x+y)	\frac{\partial\:}{\partial\:y}(x^{2}y+x+y)
limit as x approaches 1 of-x^2+5x-7	\lim\:_{x\to\:1}(-x^{2}+5x-7)
(\partial)/(\partial y)(x+ycos(x))	\frac{\partial\:}{\partial\:y}(x+y\cos(x))
f(x)=sin^5(x)	f(x)=\sin^{5}(x)
limit as x approaches 0 of cos(0)	\lim\:_{x\to\:0}(\cos(0))
integral of (x^2+1)/(e^x)	\int\:\frac{x^{2}+1}{e^{x}}dx
(dx)/(dt)+4tx^3+x/t =0	\frac{dx}{dt}+4tx^{3}+\frac{x}{t}=0
f(x)=(1-sec(x))/(tan(x))	f(x)=\frac{1-\sec(x)}{\tan(x)}
derivative of f(x)=7+2/x+5/(x^2)	derivative\:f(x)=7+\frac{2}{x}+\frac{5}{x^{2}}
integral of 1/(sqrt((x-9)(3-x)))	\int\:\frac{1}{\sqrt{(x-9)(3-x)}}dx
xy^{''}+2y^'=24x^2	xy^{\prime\:\prime\:}+2y^{\prime\:}=24x^{2}
integral of-5x	\int\:-5xdx
derivative of y=(3x^2+2)(4x-1)	derivative\:y=(3x^{2}+2)(4x-1)
derivative of (e^x/(x^2))	\frac{d}{dx}(\frac{e^{x}}{x^{2}})
integral of (2x+1)/(x^2-3x+2)	\int\:\frac{2x+1}{x^{2}-3x+2}dx
y^{''}+4y=e-t	y^{\prime\:\prime\:}+4y=e-t
integral of 8/(\sqrt[3]{x^2)}	\int\:\frac{8}{\sqrt[3]{x^{2}}}dx
y^{''}-2y^'=6e^{2x}	y^{\prime\:\prime\:}-2y^{\prime\:}=6e^{2x}
integral of (9x^2+6x+9)/(x^3-1)	\int\:\frac{9x^{2}+6x+9}{x^{3}-1}dx
laplacetransform e^{2t}sin(2tj)	laplacetransform\:e^{2t}\sin(2tj)
derivative of y=ccos(t)+t^2sin(t)	derivative\:y=c\cos(t)+t^{2}\sin(t)
(\partial)/(\partial y)(x+2y+1)	\frac{\partial\:}{\partial\:y}(x+2y+1)
laplacetransform 6cos(4t-1)	laplacetransform\:6\cos(4t-1)
integral from 0 to 3 of-2x	\int\:_{0}^{3}-2xdx
tangent of f(x)=x^4+9e^x,\at x=0	tangent\:f(x)=x^{4}+9e^{x},\at\:x=0
integral of (x^2)/(2^x)	\int\:\frac{x^{2}}{2^{x}}dx
(\partial)/(\partial x)((2+4y^2)x-3x^2)	\frac{\partial\:}{\partial\:x}((2+4y^{2})x-3x^{2})
integral of (sqrt(x^2+5))/x	\int\:\frac{\sqrt{x^{2}+5}}{x}dx
derivative of (x^2)/(5+x)	derivative\:\frac{x^{2}}{5+x}
derivative of \sqrt[10]{x}	derivative\:\sqrt[10]{x}
tangent of y=(14)/(1+e^{-x)},(0,7)	tangent\:y=\frac{14}{1+e^{-x}},(0,7)
integral of 13ln(x^2-x+6)	\int\:13\ln(x^{2}-x+6)dx
derivative of x^4+3	\frac{d}{dx}(x^{4}+3)
(\partial)/(\partial x)(x^2-y/4)	\frac{\partial\:}{\partial\:x}(x^{2}-\frac{y}{4})
sum from n=2 to infinity of 1/(n^3+n)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{3}+n}
derivative of ln(3x^2-cos(x))	\frac{d}{dx}(\ln(3x^{2}-\cos(x)))
y^'-ytan(x)=sec(x)	y^{\prime\:}-y\tan(x)=\sec(x)
derivative of (3x-3)^2(1-5x)^4	derivative\:(3x-3)^{2}(1-5x)^{4}
laplacetransform 3t+2	laplacetransform\:3t+2
y^{''}+2y+y=0	y^{\prime\:\prime\:}+2y+y=0
tangent of f(x)=(5/(x^2+1)),\at x=-1	tangent\:f(x)=(\frac{5}{x^{2}+1}),\at\:x=-1
y^'=2e^{(6x-y)}	y^{\prime\:}=2e^{(6x-y)}
integral of (x^2+x)e^{2x}	\int\:(x^{2}+x)e^{2x}dx
(\partial)/(\partial z)(2yz)	\frac{\partial\:}{\partial\:z}(2yz)
tangent of f(x)=x-4tan(x),\at x=(3pi)/4	tangent\:f(x)=x-4\tan(x),\at\:x=\frac{3π}{4}
integral of (-6sin(2x)+3cos(3x))	\int\:(-6\sin(2x)+3\cos(3x))dx
integral from-1 to 1 of sqrt(1+4x^2)	\int\:_{-1}^{1}\sqrt{1+4x^{2}}dx
integral of (sqrt(x)+3/(sqrt(x)))	\int\:(\sqrt{x}+\frac{3}{\sqrt{x}})dx
limit as x approaches-1 of (1+x)^{-1}	\lim\:_{x\to\:-1}((1+x)^{-1})
(\partial)/(\partial x)((3x-y)/((x+y)^3))	\frac{\partial\:}{\partial\:x}(\frac{3x-y}{(x+y)^{3}})
y^'=(t^2+ty+y^2)/(t^2)	y^{\prime\:}=\frac{t^{2}+ty+y^{2}}{t^{2}}
(\partial)/(\partial x)(cos^2(x+y))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x+y))
(dy}{dx}+\frac{2y)/x = 1/(x^2)	\frac{dy}{dx}+\frac{2y}{x}=\frac{1}{x^{2}}
area x^2-4,y=0,x=-4,x=3	area\:x^{2}-4,y=0,x=-4,x=3
derivative of ln(sqrt((a+bx/(a-bx))))	\frac{d}{dx}(\ln(\sqrt{\frac{a+bx}{a-bx}}))
inverse oflaplace 1/(s^2+4s+12)	inverselaplace\:\frac{1}{s^{2}+4s+12}
derivative of (7x+3^2)	\frac{d}{dx}((7x+3)^{2})
derivative of (3x^3+1(-4x^2-3)^4)	\frac{d}{dx}((3x^{3}+1)(-4x^{2}-3)^{4})
limit as x approaches 4 of (x^2-6)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{2}-6}{x-4})
integral of (sqrt(t))/(1+t)	\int\:\frac{\sqrt{t}}{1+t}dt
derivative of 14*((-x+2)/(x^2))	derivative\:14\cdot\:(\frac{-x+2}{x^{2}})
limit as x approaches 0 of (e^{7x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{7x}-1}{x})
integral of e^{3y}	\int\:e^{3y}dy
laplacetransform e^{-3t}sin(t)	laplacetransform\:e^{-3t}\sin(t)
(dy)/(dx)=((-2y)/((x-2)))	\frac{dy}{dx}=(\frac{-2y}{(x-2)})
limit as x approaches 0+of-1	\lim\:_{x\to\:0+}(-1)
integral of 6(x+2)	\int\:6(x+2)dx
limit as x approaches 0 of x/(sqrt(x^2))	\lim\:_{x\to\:0}(\frac{x}{\sqrt{x^{2}}})
integral of (ax+b)/(a^2x^2+b^2)	\int\:\frac{ax+b}{a^{2}x^{2}+b^{2}}dx
(dy)/(dx)+4y=0	\frac{dy}{dx}+4y=0
derivative of f(x)=3x^2+2x-3	derivative\:f(x)=3x^{2}+2x-3
integral of x*sin(kx)	\int\:x\cdot\:\sin(kx)dx
y^{''}-8y^'=0	y^{\prime\:\prime\:}-8y^{\prime\:}=0
derivative of 1/(ln(3x))	derivative\:\frac{1}{\ln(3x)}
integral of 3xe^{2x}	\int\:3xe^{2x}dx
y^'= 1/(2y)	y^{\prime\:}=\frac{1}{2y}
integral of 1/((x+3)sqrt(x^2+6x+5))	\int\:\frac{1}{(x+3)\sqrt{x^{2}+6x+5}}dx
limit as x approaches 2 of (x-3)^2	\lim\:_{x\to\:2}((x-3)^{2})
integral of sec^5(x	\int\:\sec^{5}(d)xdx
integral from 0 to 5 of 20e^{0.02x}	\int\:_{0}^{5}20e^{0.02x}dx
derivative of f(x)=(x^3)/(12)+1/x	derivative\:f(x)=\frac{x^{3}}{12}+\frac{1}{x}
(\partial)/(\partial y)(zy^2(t+1))	\frac{\partial\:}{\partial\:y}(zy^{2}(t+1))

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