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Popular Calculus Problems

limit as x approaches 3+of 1/(x-3)	\lim\:_{x\to\:3+}(\frac{1}{x-3})
integral from-infinity to 0 of 1/(5-3x)	\int\:_{-\infty\:}^{0}\frac{1}{5-3x}dx
y^'+ytan(t)=(tan(t))/(cos(t))	y^{\prime\:}+y\tan(t)=\frac{\tan(t)}{\cos(t)}
integral of x^3In(x)	\int\:x^{3}In(x)dx
tangent of e^t+3,\at t=0	tangent\:e^{t}+3,\at\:t=0
y^{''}+4y=sin(t)	y^{\prime\:\prime\:}+4y=\sin(t)
taylor x^{-2},6	taylor\:x^{-2},6
area y^2=x^3,y^2=x	area\:y^{2}=x^{3},y^{2}=x
integral of (-9x^2+2)/(x^3+9x)	\int\:\frac{-9x^{2}+2}{x^{3}+9x}dx
integral of 1/(x^2sqrt(x^2+49))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+49}}dx
derivative of 2/((1-1/3 x^3+1^2))	\frac{d}{dx}(\frac{2}{(1-\frac{1}{3}x^{3}+1)^{2}})
derivative of 5x^2-2x-1	derivative\:5x^{2}-2x-1
integral of (x^2)/(x^4+10x^2+9)	\int\:\frac{x^{2}}{x^{4}+10x^{2}+9}dx
y^{''}+4y^'+4y=e^{-2x}ln(x)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}\ln(x)
derivative of f(x)= 1/(7-x)	derivative\:f(x)=\frac{1}{7-x}
derivative of h(sqrt(x))	\frac{d}{dx}(h(\sqrt{x}))
derivative of f(x)= 9/(sqrt(x))	derivative\:f(x)=\frac{9}{\sqrt{x}}
(dy)/(dx)= 1/6 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{6}\sqrt{y}\cos^{2}(\sqrt{y})
integral of 11(tan(x))(ln(cos(x)))	\int\:11(\tan(x))(\ln(\cos(x)))dx
inverse oflaplace (1/7)/(s^2+19980/7)	inverselaplace\:\frac{\frac{1}{7}}{s^{2}+\frac{19980}{7}}
integral of t^{-1/2}(t^4+2t^2-1)	\int\:t^{-\frac{1}{2}}(t^{4}+2t^{2}-1)dt
integral of sin(s)	\int\:\sin(s)ds
laplacetransform-4t^2+16t+9	laplacetransform\:-4t^{2}+16t+9
(\partial)/(\partial x)(4x(2+y)^{-1})	\frac{\partial\:}{\partial\:x}(4x(2+y)^{-1})
tangent of f(x)= x/(1+x^2),\at x=2	tangent\:f(x)=\frac{x}{1+x^{2}},\at\:x=2
integral of x/(x-10)	\int\:\frac{x}{x-10}dx
area 9.86x^2,4.92x-x^2	area\:9.86x^{2},4.92x-x^{2}
(\partial)/(\partial t)(t^3)	\frac{\partial\:}{\partial\:t}(t^{3})
derivative of 5-6/x	derivative\:5-\frac{6}{x}
area sqrt(x)+2,0,1,4	area\:\sqrt{x}+2,0,1,4
derivative of e^{z/(z-2)}	derivative\:e^{\frac{z}{z-2}}
normal of f(x)=4x^2+7,(-3,43)	normal\:f(x)=4x^{2}+7,(-3,43)
81y^{''}-16y=0	81y^{\prime\:\prime\:}-16y=0
limit as x approaches 7 of 0	\lim\:_{x\to\:7}(0)
integral from 0 to 5 of x^2-5x	\int\:_{0}^{5}x^{2}-5xdx
(1+x)y^'+2y=(sin(x))/(1+x)	(1+x)y^{\prime\:}+2y=\frac{\sin(x)}{1+x}
integral of sin(5θ)sin(θ)	\int\:\sin(5θ)\sin(θ)dθ
(\partial)/(\partial x)(9xe^{4xy})	\frac{\partial\:}{\partial\:x}(9xe^{4xy})
(\partial}{\partial x}(\frac{x+y)/2)	\frac{\partial\:}{\partial\:x}(\frac{x+y}{2})
inverse oflaplace 3/((s+1)^2)	inverselaplace\:\frac{3}{(s+1)^{2}}
sum from n=1 to infinity of (4^n)/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{4^{n}}{2^{n}}
slope of xy-3y^2=8,(14,4)	slope\:xy-3y^{2}=8,(14,4)
integral of sqrt(x)e^{-sqrt(x)}	\int\:\sqrt{x}e^{-\sqrt{x}}dx
derivative of (sqrt(2x)/(ln(x)))	\frac{d}{dx}(\frac{\sqrt{2x}}{\ln(x)})
derivative of (x^3/(1-x^3))	\frac{d}{dx}(\frac{x^{3}}{1-x^{3}})
(\partial)/(\partial x)(x+e^z+y)	\frac{\partial\:}{\partial\:x}(x+e^{z}+y)
integral of 4sin(2x)-3cos(3x)	\int\:4\sin(2x)-3\cos(3x)dx
normal of f(x)=x^4+5x-2,(1,4)	normal\:f(x)=x^{4}+5x-2,(1,4)
integral of (e^{4sqrt(r)})/(sqrt(r))	\int\:\frac{e^{4\sqrt{r}}}{\sqrt{r}}dr
limit as x approaches-3-of (x+4)/(x+3)	\lim\:_{x\to\:-3-}(\frac{x+4}{x+3})
integral of 1/(7-6x)	\int\:\frac{1}{7-6x}dx
limit as x approaches 5-of (x+1)/(x-5)	\lim\:_{x\to\:5-}(\frac{x+1}{x-5})
f(x)=-cos(x)	f(x)=-\cos(x)
derivative of x(2x+1^3)	\frac{d}{dx}(x(2x+1)^{3})
tangent of f(x)=(4x^2-3x)^2,\at x=1	tangent\:f(x)=(4x^{2}-3x)^{2},\at\:x=1
integral of (x^2+20x-4)/(x^3-4x)	\int\:\frac{x^{2}+20x-4}{x^{3}-4x}dx
(\partial)/(\partial z)(xy^2e^{-xz})	\frac{\partial\:}{\partial\:z}(xy^{2}e^{-xz})
(12x^2-20y^2)dx+(-20xy+36x^{-1}y^3)dy=0	(12x^{2}-20y^{2})dx+(-20xy+36x^{-1}y^{3})dy=0
integral of e^{sqrt(x)}	\int\:e^{\sqrt{x}}dx
integral of (x^2)/(sqrt(x+2))	\int\:\frac{x^{2}}{\sqrt{x+2}}dx
normal of y=5x^3+4x^2-6,(1,3)	normal\:y=5x^{3}+4x^{2}-6,(1,3)
integral of e^{-2x}*sin(x)	\int\:e^{-2x}\cdot\:\sin(x)dx
limit as x approaches 2 of (-2)^3	\lim\:_{x\to\:2}((-2)^{3})
(\partial)/(\partial x)((xy)/((x+y)))	\frac{\partial\:}{\partial\:x}(\frac{xy}{(x+y)})
derivative of-1/(1+x^2)	\frac{d}{dx}(-\frac{1}{1+x^{2}})
d/(dy)(4y^2)	\frac{d}{dy}(4y^{2})
maclaurin ln(x+sqrt(x^2-1))	maclaurin\:\ln(x+\sqrt{x^{2}-1})
derivative of sqrt(6x+6x^2)	\frac{d}{dx}(\sqrt{6x+6x^{2}})
(dv)/(dt)=0.025*7-v/(2000),v(0)=100	\frac{dv}{dt}=0.025\cdot\:7-\frac{v}{2000},v(0)=100
integral from 4 to 10 of 0.13x	\int\:_{4}^{10}0.13xdx
integral of 7-x	\int\:7-xdx
integral of 3e^{2x}	\int\:3e^{2x}dx
(\partial)/(\partial y)(x^2y+xy^3)	\frac{\partial\:}{\partial\:y}(x^{2}y+xy^{3})
(\partial)/(\partial x)(cos(x)cos(y))	\frac{\partial\:}{\partial\:x}(\cos(x)\cos(y))
(dx)/(dt)=(457.8-7x)/(2180)	\frac{dx}{dt}=\frac{457.8-7x}{2180}
derivative of (1-e^{x^3})^5	derivative\:(1-e^{x^{3}})^{5}
limit as x approaches 1-of x^2-2	\lim\:_{x\to\:1-}(x^{2}-2)
tangent of y=(x^2-1)/(x^2+x+1),(1,0)	tangent\:y=\frac{x^{2}-1}{x^{2}+x+1},(1,0)
y^{''}+4y^'+5y=cos(2x)	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=\cos(2x)
inverse oflaplace 1/((x^2+1)*x)	inverselaplace\:\frac{1}{(x^{2}+1)\cdot\:x}
integral of xsin(1/4 x)	\int\:x\sin(\frac{1}{4}x)dx
integral of 3x^2\sqrt[3]{2x^3+5}	\int\:3x^{2}\sqrt[3]{2x^{3}+5}dx
(\partial)/(\partial s)(3sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:s}(3\sqrt{s^{2}+t^{2}})
domain of f(x)=(x^4+1)^7	domain\:f(x)=(x^{4}+1)^{7}
(dy)/(dx)=x-y,y(0)=2	\frac{dy}{dx}=x-y,y(0)=2
limit as x approaches 0 of ln(1/(x^2))	\lim\:_{x\to\:0}(\ln(\frac{1}{x^{2}}))
(\partial)/(\partial z)(y^2z)	\frac{\partial\:}{\partial\:z}(y^{2}z)
integral from 0 to N of e^{-st}cos(3t)	\int\:_{0}^{N}e^{-st}\cos(3t)dt
tangent of y=4x-3x^2,(2,-4)	tangent\:y=4x-3x^{2},(2,-4)
derivative of (x+2)^2	derivative\:(x+2)^{2}
(dy)/(dx)-1/x y=-9	\frac{dy}{dx}-\frac{1}{x}y=-9
integral of (5x^3+2x)/(x-1)	\int\:\frac{5x^{3}+2x}{x-1}dx
derivative of 2+4cos(x^3+3sin(x^3))	\frac{d}{dx}(2+4\cos(x^{3})+3\sin(x^{3}))
derivative of ln(\sqrt[4]{(x-1/(x+1)}))	\frac{d}{dx}(\ln(\sqrt[4]{\frac{x-1}{x+1}}))
derivative of f(x)= 1/5 x^2+(200000)/x	derivative\:f(x)=\frac{1}{5}x^{2}+\frac{200000}{x}
(1+x^2)y^{''}+y^'x+ax=0	(1+x^{2})y^{\prime\:\prime\:}+y^{\prime\:}x+ax=0
f(t)=3cos(t)	f(t)=3\cos(t)
integral of (sec(x))/(2sec(x)+1)	\int\:\frac{\sec(x)}{2\sec(x)+1}dx
tangent of x^2+y^2=100,(-6,8)	tangent\:x^{2}+y^{2}=100,(-6,8)
integral of-xcos((nxpi)/l)	\int\:-x\cos(\frac{nxπ}{l})dx

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