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Popular Calculus Problems

limit as x approaches 0 of (2tan(x))/x	\lim\:_{x\to\:0}(\frac{2\tan(x)}{x})
integral of 3/(1+sqrt(3x))	\int\:\frac{3}{1+\sqrt{3x}}dx
(\partial)/(\partial x)(6x^2y)	\frac{\partial\:}{\partial\:x}(6x^{2}y)
dy=(x+6)/(x+1)dx	dy=\frac{x+6}{x+1}dx
derivative of y=4sin(5x-2)	derivative\:y=4\sin(5x-2)
(t^2+1)(dy)/(dt)=yt-y	(t^{2}+1)\frac{dy}{dt}=yt-y
sum from n=1 to infinity of 1/(n8^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n8^{n}}
integral of 1/(3+25x^2)	\int\:\frac{1}{3+25x^{2}}dx
integral of cot^6(x)	\int\:\cot^{6}(x)dx
f(t)=\sqrt[4]{t}	f(t)=\sqrt[4]{t}
slope of (-7.6)(4.2)	slope\:(-7.6)(4.2)
d/(dt)(t/(t-1))	\frac{d}{dt}(\frac{t}{t-1})
derivative of (x^6/(3-x^5))	\frac{d}{dx}(\frac{x^{6}}{3-x^{5}})
derivative of 4te^{-t}	derivative\:4te^{-t}
limit as x approaches-1 of 1+e^{1/x}	\lim\:_{x\to\:-1}(1+e^{\frac{1}{x}})
integral from 2 to 4 of (-x^2+6x-8)	\int\:_{2}^{4}(-x^{2}+6x-8)dx
derivative of x^3(8x^2+2x-3^2)	\frac{d}{dx}(x^{3}(8x^{2}+2x-3)^{2})
limit as x approaches+0 of (2x+1)/(x^3)	\lim\:_{x\to\:+0}(\frac{2x+1}{x^{3}})
(\partial)/(\partial y)(xye^{-3y})	\frac{\partial\:}{\partial\:y}(xye^{-3y})
area x^2-3x,5x,[0,8]	area\:x^{2}-3x,5x,[0,8]
area x^2-1,0,2	area\:x^{2}-1,0,2
integral from 0 to 4 of 3t-8	\int\:_{0}^{4}3t-8dt
(dy)/(dx)+y=2xy^2ex	\frac{dy}{dx}+y=2xy^{2}ex
inverse oflaplace 1/(4s+1)	inverselaplace\:\frac{1}{4s+1}
derivative of (4x-x^2/(6-x))	\frac{d}{dx}(\frac{4x-x^{2}}{6-x})
tangent of f(x)=sqrt((2x-6)/(x-1))	tangent\:f(x)=\sqrt{\frac{2x-6}{x-1}}
(dy)/(dx)=y^{1/2}	\frac{dy}{dx}=y^{\frac{1}{2}}
integral of (72)/(1-cos(8x))	\int\:\frac{72}{1-\cos(8x)}dx
derivative of e^{-x^4}	derivative\:e^{-x^{4}}
integral of 1/((8x+9)^2)	\int\:\frac{1}{(8x+9)^{2}}dx
sum from n=1 to infinity of (-4)^n	\sum\:_{n=1}^{\infty\:}(-4)^{n}
integral of sec(x)tan(x)-4e^x	\int\:\sec(x)\tan(x)-4e^{x}dx
integral of sinh(4x)	\int\:\sinh(4x)dx
taylor (1+(1/2)*x)-4	taylor\:(1+(\frac{1}{2})\cdot\:x)-4
limit as t approaches 0 of e^{5t}	\lim\:_{t\to\:0}(e^{5t})
(d^2)/(dx^2)(sqrt(r)+\sqrt[5]{r})	\frac{d^{2}}{dx^{2}}(\sqrt{r}+\sqrt[5]{r})
derivative of e^{x^2-3}	\frac{d}{dx}(e^{x^{2}-3})
integral from 0 to 1 of sqrt(1+9x)	\int\:_{0}^{1}\sqrt{1+9x}dx
d/(dt)(10sin(t))	\frac{d}{dt}(10\sin(t))
d/(dt)(ln(-ln(1-t)))	\frac{d}{dt}(\ln(-\ln(1-t)))
(\partial)/(\partial y)(4x-y)	\frac{\partial\:}{\partial\:y}(4x-y)
integral from 4 to 16 of (3sqrt(x))	\int\:_{4}^{16}(3\sqrt{x})dx
derivative of ((x-y)/((x+y)))	\frac{d}{dx}(\frac{(x-y)}{(x+y)})
integral of xsin((x^2)/2)	\int\:x\sin(\frac{x^{2}}{2})dx
integral of 2/(7x)	\int\:\frac{2}{7x}dx
(dy)/(dx)= x/(49y)	\frac{dy}{dx}=\frac{x}{49y}
(d^2y)/(dt^2)+4(dy)/(dt)+4y=0	\frac{d^{2}y}{dt^{2}}+4\frac{dy}{dt}+4y=0
integral of 1/(e^x+1)	\int\:\frac{1}{e^{x}+1}dx
(\partial)/(\partial t)(s*cos(t))	\frac{\partial\:}{\partial\:t}(s\cdot\:\cos(t))
d/(dy)(sqrt(1+y^2))	\frac{d}{dy}(\sqrt{1+y^{2}})
tangent of f(x)=2x^2+4,\at x=-2	tangent\:f(x)=2x^{2}+4,\at\:x=-2
limit as z approaches 1+i of z^2-5z+10	\lim\:_{z\to\:1+i}(z^{2}-5z+10)
y^'=2y-4x	y^{\prime\:}=2y-4x
limit as x approaches-3 of x/(x+3)	\lim\:_{x\to\:-3}(\frac{x}{x+3})
limit as x approaches 0 of (x-xcos(x))/(sin^2(3x))	\lim\:_{x\to\:0}(\frac{x-x\cos(x)}{\sin^{2}(3x)})
derivative of 2x^3-3x^2-36x	\frac{d}{dx}(2x^{3}-3x^{2}-36x)
limit as x approaches-infinity of 2/x-3	\lim\:_{x\to\:-\infty\:}(\frac{2}{x}-3)
limit as n approaches infinity of 1/2	\lim\:_{n\to\:\infty\:}(\frac{1}{2})
integral of x^3*e^{-x}	\int\:x^{3}\cdot\:e^{-x}dx
tangent of f(x)= 5/x ,(-3,(-5/3))	tangent\:f(x)=\frac{5}{x},(-3,(-\frac{5}{3}))
(dx)/(dt)+3=0	\frac{dx}{dt}+3=0
derivative of y=sqrt(4+csc(t^4))	derivative\:y=\sqrt{4+\csc(t^{4})}
derivative of y=((x-1)/(x^2+x+1))^4	derivative\:y=(\frac{x-1}{x^{2}+x+1})^{4}
y^'+2xy=2x	y^{\prime\:}+2xy=2x
integral of 5e^xsqrt(1+e^x)	\int\:5e^{x}\sqrt{1+e^{x}}dx
limit as x approaches-9 of (x^2-3)/(9-x)	\lim\:_{x\to\:-9}(\frac{x^{2}-3}{9-x})
integral from 0 to pi/2 of 12cos^5(x)	\int\:_{0}^{\frac{π}{2}}12\cos^{5}(x)dx
integral of (x^3)/(sqrt(3x^2+\sqrt{2))}	\int\:\frac{x^{3}}{\sqrt{3x^{2}+\sqrt{2}}}dx
inverse oflaplace s/(s(s+1))	inverselaplace\:\frac{s}{s(s+1)}
integral of (e^{8/x})/(x^2)	\int\:\frac{e^{\frac{8}{x}}}{x^{2}}dx
derivative of-2sec^2(xtan(x))	\frac{d}{dx}(-2\sec^{2}(x)\tan(x))
limit as x approaches 0 of-csc^2(x)	\lim\:_{x\to\:0}(-\csc^{2}(x))
derivative of 3a^{3x}	\frac{d}{dx}(3a^{3x})
derivative of y=sin^5(3x)	derivative\:y=\sin^{5}(3x)
integral of sqrt(2x+3)	\int\:\sqrt{2x+3}dx
derivative of sqrt(5-6x)	\frac{d}{dx}(\sqrt{5-6x})
integral of sqrt(x)(x+3)	\int\:\sqrt{x}(x+3)dx
derivative of 3x^2-27	\frac{d}{dx}(3x^{2}-27)
sum from n=1 to infinity of 1/((2n-1)^6)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n-1)^{6}}
integral from 0 to ln(3) of e^{2x}	\int\:_{0}^{\ln(3)}e^{2x}dx
limit as x approaches 0+of 3x^{x/2}	\lim\:_{x\to\:0+}(3x^{\frac{x}{2}})
area y=3x,y=9x^2	area\:y=3x,y=9x^{2}
y^{''}+4y=9e^{2t}sin(2t)+5t^2	y^{\prime\:\prime\:}+4y=9e^{2t}\sin(2t)+5t^{2}
tangent of sec(x)	tangent\:\sec(x)
limit as x approaches 0 of arctan(x)	\lim\:_{x\to\:0}(\arctan(x))
inverse oflaplace (s-1)/(s^2-2s+1)	inverselaplace\:\frac{s-1}{s^{2}-2s+1}
(\partial)/(\partial y)(ln(x+6y+5z))	\frac{\partial\:}{\partial\:y}(\ln(x+6y+5z))
integral of (10)/((x+1)(x^2+9)^2)	\int\:\frac{10}{(x+1)(x^{2}+9)^{2}}dx
limit as x approaches 8-of (x-8)/(\|x-8\|)	\lim\:_{x\to\:8-}(\frac{x-8}{\left\|x-8\right\|})
derivative of 2(4-9x^4)	\frac{d}{dx}(2(4-9x)^{4})
(xy+y+y^2)dx+(x+2y)dy=0	(xy+y+y^{2})dx+(x+2y)dy=0
tangent of f(x)=sqrt(x-5),\at x=6	tangent\:f(x)=\sqrt{x-5},\at\:x=6
area x=7y^3,x=18y^2	area\:x=7y^{3},x=18y^{2}
integral of ge^{-cx}	\int\:ge^{-cx}dx
tangent of f(x)=ln(x^2-2x+1),\at x=2	tangent\:f(x)=\ln(x^{2}-2x+1),\at\:x=2
derivative of ((x^2))/(2+x)	derivative\:\frac{(x^{2})}{2+x}
integral of e^{-0.06x}	\int\:e^{-0.06x}dx
(\partial)/(\partial y)(sin(x-y)+(xy))	\frac{\partial\:}{\partial\:y}(\sin(x-y)+(xy))
(\partial)/(\partial x)(-4x^2y-4x)	\frac{\partial\:}{\partial\:x}(-4x^{2}y-4x)
derivative of (x^2+4x+8/((x+2)^2))	\frac{d}{dx}(\frac{x^{2}+4x+8}{(x+2)^{2}})

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