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Popular Calculus Problems

0.145(dv)/(dt)=(0.1459.81)-(0.043*v)	0.145\cdot\:\frac{dv}{dt}=(0.145\cdot\:9.81)-(0.043\cdot\:v)
limit as (x,y) approaches (0,0) of \|x+y\|	\lim\:_{(x,y)\to\:(0,0)}(\left\|x+y\right\|)
integral of (2e^x+e^{2x})/(e^x)	\int\:\frac{2e^{x}+e^{2x}}{e^{x}}dx
limit as x approaches+2 of (5x)/(x-2)	\lim\:_{x\to\:+2}(\frac{5x}{x-2})
integral of-(12)/y	\int\:-\frac{12}{y}dy
(\partial)/(\partial x)(-3xysin(z))	\frac{\partial\:}{\partial\:x}(-3xy\sin(z))
derivative of 1/9 ln(-ln(x)+5)	\frac{d}{dx}(\frac{1}{9}\ln(-\ln(x))+5)
x(dy)/(dx)+3y=2x^5	x\frac{dy}{dx}+3y=2x^{5}
integral of (3x+6)/(x^2+2x+2)	\int\:\frac{3x+6}{x^{2}+2x+2}dx
integral from 0 to 4 of sqrt(x)+3x	\int\:_{0}^{4}\sqrt{x}+3xdx
integral of (x^6-x^3+64)/(x^4+8x^2)	\int\:\frac{x^{6}-x^{3}+64}{x^{4}+8x^{2}}dx
derivative of 1-ln(1-x)	\frac{d}{dx}(1-\ln(1-x))
derivative of 6xy-12	\frac{d}{dx}(6xy-12)
integral of 1/(2x-3)	\int\:\frac{1}{2x-3}dx
derivative of-arctan(x+2arccot(x)-ln(x))	\frac{d}{dx}(-\arctan(x)+2\arccot(x)-\ln(x))
integral of 6/(xln(2x))	\int\:\frac{6}{x\ln(2x)}dx
(\partial)/(\partial x)(arcsin(y/x))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{y}{x}))
derivative of (3-e^{-x}^2)	\frac{d}{dx}((3-e^{-x})^{2})
sum from n=1 to infinity of 5/(2^n+1)	\sum\:_{n=1}^{\infty\:}\frac{5}{2^{n}+1}
(\partial)/(\partial x)(((xy))/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{(xy)}{x+y})
integral from-infinity to-1 of e^{-24t}	\int\:_{-\infty\:}^{-1}e^{-24t}dt
integral of 15sqrt(x)	\int\:15\sqrt{x}dx
integral from 0 to 1 of 1/(x^{-1)}	\int\:_{0}^{1}\frac{1}{x^{-1}}dx
integral of (5/x)	\int\:(\frac{5}{x})dx
derivative of sin(7x)+cos(2x)	derivative\:\sin(7x)+\cos(2x)
integral of 8sin^3(t)cos(t)	\int\:8\sin^{3}(t)\cos(t)dt
integral of (3x)/(x^2+2)	\int\:\frac{3x}{x^{2}+2}dx
derivative of f(x)=(3x^3)^{0.5}	derivative\:f(x)=(3x^{3})^{0.5}
(\partial)/(\partial y)(xy^3-x^2y)	\frac{\partial\:}{\partial\:y}(xy^{3}-x^{2}y)
2sqrt(x)y^'=cos^2(y)	2\sqrt{x}y^{\prime\:}=\cos^{2}(y)
derivative of-6sqrt(s)	derivative\:-6\sqrt{s}
limit as x approaches-3 of 1/(x^2-9)	\lim\:_{x\to\:-3}(\frac{1}{x^{2}-9})
taylor 1/(2+x),0	taylor\:\frac{1}{2+x},0
y^{''}+y=5sin(x)	y^{\prime\:\prime\:}+y=5\sin(x)
(dy)/(dx)x-xe^x+y=0	\frac{dy}{dx}x-xe^{x}+y=0
(dy)/(dx)=x+1	\frac{dy}{dx}=x+1
limit as x approaches 0 of c/x	\lim\:_{x\to\:0}(\frac{c}{x})
derivative of x^8(x-1)^7	derivative\:x^{8}(x-1)^{7}
integral of tcsc(t)cot(t)	\int\:t\csc(t)\cot(t)dt
derivative of 5/(cos^2(x))	\frac{d}{dx}(\frac{5}{\cos^{2}(x)})
limit as x approaches 2-of 7/(x-2)	\lim\:_{x\to\:2-}(\frac{7}{x-2})
derivative of f(x)=sqrt(3x^2+3x+3)	derivative\:f(x)=\sqrt{3x^{2}+3x+3}
integral of e^x(1+e^{1-x})	\int\:e^{x}(1+e^{1-x})dx
xy^'+6x^2y=xe^{5x}	xy^{\prime\:}+6x^{2}y=xe^{5x}
integral of sec(x)tan^2(x)	\int\:\sec(x)\tan^{2}(x)dx
integral of ((x-2))/((x^2-4x+3)^3)	\int\:\frac{(x-2)}{(x^{2}-4x+3)^{3}}dx
inverse oflaplace (12)/s	inverselaplace\:\frac{12}{s}
integral from 0 to 3 of x-1	\int\:_{0}^{3}x-1dx
taylor f(x)= 1/x	taylor\:f(x)=\frac{1}{x}
integral from-2 to 3 of (11)/(x^4)	\int\:_{-2}^{3}\frac{11}{x^{4}}dx
integral of 1/((x+2)^2(x-3))	\int\:\frac{1}{(x+2)^{2}(x-3)}dx
integral of 2cos(2t)	\int\:2\cos(2t)dt
derivative of 7+3e^{5x}	\frac{d}{dx}(7+3e^{5x})
limit as (x,y) approaches (0,69) of x^3y	\lim\:_{(x,y)\to\:(0,69)}(x^{3}y)
derivative of 14^x	derivative\:14^{x}
limit as x approaches-2 of (4-x^2)/(2+x)	\lim\:_{x\to\:-2}(\frac{4-x^{2}}{2+x})
derivative of f(x)=2e^x+8/(\sqrt[3]{x)}	derivative\:f(x)=2e^{x}+\frac{8}{\sqrt[3]{x}}
integral of e^{y^{88}}	\int\:e^{y^{88}}dy
tangent of f(x)=4x^3-7x^2-15x+10	tangent\:f(x)=4x^{3}-7x^{2}-15x+10
tangent of y=7x-4sqrt(x),(1,3)	tangent\:y=7x-4\sqrt{x},(1,3)
(y/x+5x)dx+(ln(x)-2)dy=0	(\frac{y}{x}+5x)dx+(\ln(x)-2)dy=0
derivative of 0.08e^xx^2	derivative\:0.08e^{x}x^{2}
derivative of sqrt(20x)	\frac{d}{dx}(\sqrt{20x})
integral of 5e^{3x+e^{3x}}	\int\:5e^{3x+e^{3x}}dx
derivative of f(x)=sec^3(x)	derivative\:f(x)=\sec^{3}(x)
integral of (t^2+2)	\int\:(t^{2}+2)dt
integral of (e^x)/(e^x(e^x-3))	\int\:\frac{e^{x}}{e^{x}(e^{x}-3)}dx
derivative of ((2x)^3)/5	derivative\:\frac{(2x)^{3}}{5}
(dy)/(dx)(y+4)=2xy+4y	\frac{dy}{dx}(y+4)=2xy+4y
(xy^'-y)cos(y/x)+x=0	(xy^{\prime\:}-y)\cos(\frac{y}{x})+x=0
derivative of cos((x^3/(10)))	\frac{d}{dx}(\cos(\frac{x^{3}}{10}))
(dy)/(dx)=((x-3)^2)/(sqrt(x))	\frac{dy}{dx}=\frac{(x-3)^{2}}{\sqrt{x}}
x*(dy)/(dx)= 1/(y^2)+y	x\cdot\:\frac{dy}{dx}=\frac{1}{y^{2}}+y
sum from n=1 to infinity of 1/(n^2+5n+6)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+5n+6}
derivative of 4+ln(x)	\frac{d}{dx}(4+\ln(x))
y^'=y(xy^6+1)	y^{\prime\:}=y(xy^{6}+1)
integral from 0 to 17 of 2pix(17x-x^2)	\int\:_{0}^{17}2πx(17x-x^{2})dx
limit as x approaches a of (sec(x)-sec(a))/(x-a)	\lim\:_{x\to\:a}(\frac{\sec(x)-\sec(a)}{x-a})
area y=6-ln(x+1),y=ln(x+1),x=0	area\:y=6-\ln(x+1),y=\ln(x+1),x=0
integral of a/((a^2+x^2)^{3/2)}	\int\:\frac{a}{(a^{2}+x^{2})^{\frac{3}{2}}}dx
integral from 3 to 6 of x/(3sqrt(x^2-8))	\int\:_{3}^{6}\frac{x}{3\sqrt{x^{2}-8}}dx
integral of 3(x+10)e^x	\int\:3(x+10)e^{x}dx
derivative of e^{(x/2})	\frac{d}{dx}(e^{(\frac{x}{2})})
limit as x approaches 0-of (24)/(tan(x))	\lim\:_{x\to\:0-}(\frac{24}{\tan(x)})
limit as x approaches 1+of x	\lim\:_{x\to\:1+}(x)
derivative of (1+x^2arctan(x))	\frac{d}{dx}((1+x^{2})\arctan(x))
derivative of x^3y-y^2	derivative\:x^{3}y-y^{2}
integral of (tan(4x)+sec(4x))^2	\int\:(\tan(4x)+\sec(4x))^{2}dx
(\partial)/(\partial x)(e^{3x-y})	\frac{\partial\:}{\partial\:x}(e^{3x-y})
tangent of f(x)=3e^{1-x^2},(1,3)	tangent\:f(x)=3e^{1-x^{2}},(1,3)
sum from n=0 to infinity of-1/(5^n)	\sum\:_{n=0}^{\infty\:}-\frac{1}{5^{n}}
11x^2y+(dy)/(dx)=-6x^2	11x^{2}y+\frac{dy}{dx}=-6x^{2}
limit as x approaches-5 of (x+5)/(x+5)	\lim\:_{x\to\:-5}(\frac{x+5}{x+5})
integral of ln(x^{-2})	\int\:\ln(x^{-2})dx
limit as x approaches-4 of 1/4 x^5-2x	\lim\:_{x\to\:-4}(\frac{1}{4}x^{5}-2x)
derivative of sqrt(r)+\sqrt[3]{r}	derivative\:\sqrt{r}+\sqrt[3]{r}
integral of 1000-50x	\int\:1000-50xdx
derivative of (arctan(2x))^2	derivative\:(\arctan(2x))^{2}
area x=3y,x=y^2-10	area\:x=3y,x=y^{2}-10
integral from 0 to R of x/(1+x^2)	\int\:_{0}^{R}\frac{x}{1+x^{2}}dx

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